AustralieFrV1, PascalFrancis, Curation, bibRecord, 002E60

Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

Identifieur interne : 002E60 ( PascalFrancis/Curation ); précédent : 002E59; suivant : 002E61

Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

Auteurs : S. Boukraa [Algérie] ; A. J. Guttmann [Australie] ; S. Hassani [Algérie] ; I. Jensen [Australie] ; J-M. Maillard [France] ; B. Nickel [Canada] ; N. Zenine [Algérie]

Source :

Journal of physics. A, Mathematical and theoretical : (Print) [ 1751-8113 ] ; 2008.

RBID : Pascal:08-0524292

Descripteurs français

Pascal (Inist)
- Susceptibilité magnétique, Réseau carré, Modèle réticulaire, Modèle Ising, Basse température, Haute température, Algorithme, Equation différentielle, Singularité, Loi puissance, Comportement critique, Spectre puissance, Analyse spectre.

English descriptors

KwdEn :
- Algorithms, Critical behavior, Differential equations, High temperature, Ising model, Lattice model, Low temperature, Magnetic susceptibility, Power law, Power spectra, Singularity, Spectrum analysis, Square lattices.

Abstract

We calculate very long low- and high-temperature series for the susceptibility X of the square lattice Ising model as well as very long series for the five-particle contribution X⁽⁵⁾ and six-particle contribution X⁽⁶⁾. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150 000 CPU hours on computer clusters. The series for / (low- and high-temperature regimes), X⁽⁵⁾ and X⁽⁶⁾ are now extended to 2000 terms. In addition, for X⁽⁵⁾, 10000 terms of the series are calculated modulo a single prime, and have been used to find the linear ODE satisfied by X⁽⁵⁾ modulo a prime. A diff-Padé analysis of the 2000 terms series for X⁽⁵⁾ and X⁽⁶⁾ confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the n-particle components of the susceptibility, up to a small set of 'additional' singularities. The exponents at all the singularities of the Fuchsian linear ODE of X⁽⁵⁾ and the (as yet unknown) ODE of X⁽⁶⁾ are given: they are all rational numbers. We find the presence of singularities at w = 1/2 for the linear ODE of X⁽⁵⁾, and w² = 1/8 for the ODE of X⁽⁶⁾, which are not singularities of the 'physical' X⁽⁵⁾ and X⁽⁶⁾, that is to say the series solutions of the ODE's which are analytic at w = 0. Furthermore, analysis of the long series for X⁽⁵⁾ (and X⁽⁶⁾) combined with the corresponding long series for the full susceptibility X yields previously conjectured singularities in some X⁽ⁿ⁾, n ≥ 7. The exponents at all these singularities are also seen to be rational numbers. We also present a mechanism of resummation of the logarithmic singularities of the X⁽ⁿ⁾ leading to the known power-law critical behaviour occurring in the full X, and perform a power spectrum analysis giving strong arguments in favour of the existence of a natural boundary for the full susceptibility X.

A01	`01`	`1`		`@0 1751-8113`
A03		`1`		`@0 J. phys., A, math. theor. : (Print)`
A05				`@2 41`
A06				`@2 45`
A08	`01`	`1`	`ENG`	`@1 Experimental mathematics on the magnetic susceptibility of the square lattice Ising model`
A11	`01`	`1`		`@1 BOUKRAA (S.)`
A11	`02`	`1`		`@1 GUTTMANN (A. J.)`
A11	`03`	`1`		`@1 HASSANI (S.)`
A11	`04`	`1`		`@1 JENSEN (I.)`
A11	`05`	`1`		`@1 MAILLARD (J-M.)`
A11	`06`	`1`		`@1 NICKEL (B.)`
A11	`07`	`1`		`@1 ZENINE (N.)`
A14	`01`			`@1 LPTHIRM and Département d'Aéronautique, Université de Blida @3 DZA @Z 1 aut.`
A14	`02`			`@1 ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne @2 Victoria 3010 @3 AUS @Z 2 aut. @Z 4 aut.`
A14	`03`			`@1 Centre de Recherche Nucléaire d'Alger, 2 Bd. Frantz Fanon, BP 399 @2 16000 Alger @3 DZA @Z 3 aut. @Z 7 aut.`
A14	`04`			`@1 LPTMC, Université de Paris, Tour 24, 4ème étage, case 121, 4 Place Jussieu @2 75252 Paris @3 FRA @Z 5 aut.`
A14	`05`			`@1 Department of Physics, University of Guelph @2 Guelph, Ontario NIG 2W1 @3 CAN @Z 6 aut.`
A20				`@2 455202.1-455202.51`
A21				`@1 2008`
A23	`01`			`@0 ENG`
A43	`01`			`@1 INIST @2 577C @5 354000183900970040`
A44				`@0 0000 @1 © 2008 INIST-CNRS. All rights reserved.`
A45				`@0 33 ref.`
A47	`01`	`1`		`@0 08-0524292`
A60				`@1 P`
A61				`@0 A`
A64	`01`	`1`		`@0 Journal of physics. A, Mathematical and theoretical : (Print)`
A66	`01`			`@0 GBR`
C01	`01`		`ENG`	@0 We calculate very long low- and high-temperature series for the susceptibility X of the square lattice Ising model as well as very long series for the five-particle contribution X⁽⁵⁾ and six-particle contribution X⁽⁶⁾. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150 000 CPU hours on computer clusters. The series for / (low- and high-temperature regimes), X⁽⁵⁾ and X⁽⁶⁾ are now extended to 2000 terms. In addition, for X⁽⁵⁾, 10000 terms of the series are calculated modulo a single prime, and have been used to find the linear ODE satisfied by X⁽⁵⁾ modulo a prime. A diff-Padé analysis of the 2000 terms series for X⁽⁵⁾ and X⁽⁶⁾ confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the n-particle components of the susceptibility, up to a small set of 'additional' singularities. The exponents at all the singularities of the Fuchsian linear ODE of X⁽⁵⁾ and the (as yet unknown) ODE of X⁽⁶⁾ are given: they are all rational numbers. We find the presence of singularities at w = 1/2 for the linear ODE of X⁽⁵⁾, and w² = 1/8 for the ODE of X⁽⁶⁾, which are not singularities of the 'physical' X⁽⁵⁾ and X⁽⁶⁾, that is to say the series solutions of the ODE's which are analytic at w = 0. Furthermore, analysis of the long series for X⁽⁵⁾ (and X⁽⁶⁾) combined with the corresponding long series for the full susceptibility X yields previously conjectured singularities in some X⁽ⁿ⁾, n ≥ 7. The exponents at all these singularities are also seen to be rational numbers. We also present a mechanism of resummation of the logarithmic singularities of the X⁽ⁿ⁾ leading to the known power-law critical behaviour occurring in the full X, and perform a power spectrum analysis giving strong arguments in favour of the existence of a natural boundary for the full susceptibility X.
C02	`01`	`3`		`@0 001B00`
C03	`01`	`3`	`FRE`	`@0 Susceptibilité magnétique @5 26`
C03	`01`	`3`	`ENG`	`@0 Magnetic susceptibility @5 26`
C03	`02`	`3`	`FRE`	`@0 Réseau carré @5 27`
C03	`02`	`3`	`ENG`	`@0 Square lattices @5 27`
C03	`03`	`X`	`FRE`	`@0 Modèle réticulaire @5 28`
C03	`03`	`X`	`ENG`	`@0 Lattice model @5 28`
C03	`03`	`X`	`SPA`	`@0 Modelo reticular @5 28`
C03	`04`	`3`	`FRE`	`@0 Modèle Ising @5 29`
C03	`04`	`3`	`ENG`	`@0 Ising model @5 29`
C03	`05`	`X`	`FRE`	`@0 Basse température @5 30`
C03	`05`	`X`	`ENG`	`@0 Low temperature @5 30`
C03	`05`	`X`	`SPA`	`@0 Baja temperatura @5 30`
C03	`06`	`X`	`FRE`	`@0 Haute température @5 31`
C03	`06`	`X`	`ENG`	`@0 High temperature @5 31`
C03	`06`	`X`	`SPA`	`@0 Alta temperatura @5 31`
C03	`07`	`3`	`FRE`	`@0 Algorithme @5 32`
C03	`07`	`3`	`ENG`	`@0 Algorithms @5 32`
C03	`08`	`3`	`FRE`	`@0 Equation différentielle @5 33`
C03	`08`	`3`	`ENG`	`@0 Differential equations @5 33`
C03	`09`	`3`	`FRE`	`@0 Singularité @5 34`
C03	`09`	`3`	`ENG`	`@0 Singularity @5 34`
C03	`10`	`X`	`FRE`	`@0 Loi puissance @5 35`
C03	`10`	`X`	`ENG`	`@0 Power law @5 35`
C03	`10`	`X`	`SPA`	`@0 Ley poder @5 35`
C03	`11`	`X`	`FRE`	`@0 Comportement critique @5 36`
C03	`11`	`X`	`ENG`	`@0 Critical behavior @5 36`
C03	`11`	`X`	`SPA`	`@0 Comportamiento crítico @5 36`
C03	`12`	`3`	`FRE`	`@0 Spectre puissance @5 37`
C03	`12`	`3`	`ENG`	`@0 Power spectra @5 37`
C03	`13`	`X`	`FRE`	`@0 Analyse spectre @5 38`
C03	`13`	`X`	`ENG`	`@0 Spectrum analysis @5 38`
C03	`13`	`X`	`SPA`	`@0 Análisis espectro @5 38`
N21				`@1 343`
N44	`01`			`@1 OTO`
N82				`@1 OTO`

Links toward previous steps (curation, corpus...)

to stream PascalFrancis, to step Corpus: Pour aller vers cette notice dans l'étape Curation :003193

Links to Exploration step

Pascal:08-0524292

Le document en format XML

<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">Experimental mathematics on the magnetic susceptibility of the square lattice Ising model</title>
<author><name sortKey="Boukraa, S" sort="Boukraa, S" uniqKey="Boukraa S" first="S." last="Boukraa">S. Boukraa</name>
<affiliation wicri:level="1"><inist:fA14 i1="01"><s1>LPTHIRM and Département d'Aéronautique, Université de Blida</s1>
<s3>DZA</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
<country>Algérie</country>
</affiliation>
</author>
<author><name sortKey="Guttmann, A J" sort="Guttmann, A J" uniqKey="Guttmann A" first="A. J." last="Guttmann">A. J. Guttmann</name>
<affiliation wicri:level="1"><inist:fA14 i1="02"><s1>ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne</s1>
<s2>Victoria 3010</s2>
<s3>AUS</s3>
<sZ>2 aut.</sZ>
<sZ>4 aut.</sZ>
</inist:fA14>
<country>Australie</country>
</affiliation>
</author>
<author><name sortKey="Hassani, S" sort="Hassani, S" uniqKey="Hassani S" first="S." last="Hassani">S. Hassani</name>
<affiliation wicri:level="1"><inist:fA14 i1="03"><s1>Centre de Recherche Nucléaire d'Alger, 2 Bd. Frantz Fanon, BP 399</s1>
<s2>16000 Alger</s2>
<s3>DZA</s3>
<sZ>3 aut.</sZ>
<sZ>7 aut.</sZ>
</inist:fA14>
<country>Algérie</country>
</affiliation>
</author>
<author><name sortKey="Jensen, I" sort="Jensen, I" uniqKey="Jensen I" first="I." last="Jensen">I. Jensen</name>
<affiliation wicri:level="1"><inist:fA14 i1="02"><s1>ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne</s1>
<s2>Victoria 3010</s2>
<s3>AUS</s3>
<sZ>2 aut.</sZ>
<sZ>4 aut.</sZ>
</inist:fA14>
<country>Australie</country>
</affiliation>
</author>
<author><name sortKey="Maillard, J M" sort="Maillard, J M" uniqKey="Maillard J" first="J-M." last="Maillard">J-M. Maillard</name>
<affiliation wicri:level="1"><inist:fA14 i1="04"><s1>LPTMC, Université de Paris, Tour 24, 4ème étage, case 121, 4 Place Jussieu</s1>
<s2>75252 Paris</s2>
<s3>FRA</s3>
<sZ>5 aut.</sZ>
</inist:fA14>
<country>France</country>
</affiliation>
</author>
<author><name sortKey="Nickel, B" sort="Nickel, B" uniqKey="Nickel B" first="B." last="Nickel">B. Nickel</name>
<affiliation wicri:level="1"><inist:fA14 i1="05"><s1>Department of Physics, University of Guelph</s1>
<s2>Guelph, Ontario NIG 2W1</s2>
<s3>CAN</s3>
<sZ>6 aut.</sZ>
</inist:fA14>
<country>Canada</country>
</affiliation>
</author>
<author><name sortKey="Zenine, N" sort="Zenine, N" uniqKey="Zenine N" first="N." last="Zenine">N. Zenine</name>
<affiliation wicri:level="1"><inist:fA14 i1="03"><s1>Centre de Recherche Nucléaire d'Alger, 2 Bd. Frantz Fanon, BP 399</s1>
<s2>16000 Alger</s2>
<s3>DZA</s3>
<sZ>3 aut.</sZ>
<sZ>7 aut.</sZ>
</inist:fA14>
<country>Algérie</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">INIST</idno>
<idno type="inist">08-0524292</idno>
<date when="2008">2008</date>
<idno type="stanalyst">PASCAL 08-0524292 INIST</idno>
<idno type="RBID">Pascal:08-0524292</idno>
<idno type="wicri:Area/PascalFrancis/Corpus">003193</idno>
<idno type="wicri:Area/PascalFrancis/Curation">002E60</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Experimental mathematics on the magnetic susceptibility of the square lattice Ising model</title>
<author><name sortKey="Boukraa, S" sort="Boukraa, S" uniqKey="Boukraa S" first="S." last="Boukraa">S. Boukraa</name>
<affiliation wicri:level="1"><inist:fA14 i1="01"><s1>LPTHIRM and Département d'Aéronautique, Université de Blida</s1>
<s3>DZA</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
<country>Algérie</country>
</affiliation>
</author>
<author><name sortKey="Guttmann, A J" sort="Guttmann, A J" uniqKey="Guttmann A" first="A. J." last="Guttmann">A. J. Guttmann</name>
<affiliation wicri:level="1"><inist:fA14 i1="02"><s1>ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne</s1>
<s2>Victoria 3010</s2>
<s3>AUS</s3>
<sZ>2 aut.</sZ>
<sZ>4 aut.</sZ>
</inist:fA14>
<country>Australie</country>
</affiliation>
</author>
<author><name sortKey="Hassani, S" sort="Hassani, S" uniqKey="Hassani S" first="S." last="Hassani">S. Hassani</name>
<affiliation wicri:level="1"><inist:fA14 i1="03"><s1>Centre de Recherche Nucléaire d'Alger, 2 Bd. Frantz Fanon, BP 399</s1>
<s2>16000 Alger</s2>
<s3>DZA</s3>
<sZ>3 aut.</sZ>
<sZ>7 aut.</sZ>
</inist:fA14>
<country>Algérie</country>
</affiliation>
</author>
<author><name sortKey="Jensen, I" sort="Jensen, I" uniqKey="Jensen I" first="I." last="Jensen">I. Jensen</name>
<affiliation wicri:level="1"><inist:fA14 i1="02"><s1>ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne</s1>
<s2>Victoria 3010</s2>
<s3>AUS</s3>
<sZ>2 aut.</sZ>
<sZ>4 aut.</sZ>
</inist:fA14>
<country>Australie</country>
</affiliation>
</author>
<author><name sortKey="Maillard, J M" sort="Maillard, J M" uniqKey="Maillard J" first="J-M." last="Maillard">J-M. Maillard</name>
<affiliation wicri:level="1"><inist:fA14 i1="04"><s1>LPTMC, Université de Paris, Tour 24, 4ème étage, case 121, 4 Place Jussieu</s1>
<s2>75252 Paris</s2>
<s3>FRA</s3>
<sZ>5 aut.</sZ>
</inist:fA14>
<country>France</country>
</affiliation>
</author>
<author><name sortKey="Nickel, B" sort="Nickel, B" uniqKey="Nickel B" first="B." last="Nickel">B. Nickel</name>
<affiliation wicri:level="1"><inist:fA14 i1="05"><s1>Department of Physics, University of Guelph</s1>
<s2>Guelph, Ontario NIG 2W1</s2>
<s3>CAN</s3>
<sZ>6 aut.</sZ>
</inist:fA14>
<country>Canada</country>
</affiliation>
</author>
<author><name sortKey="Zenine, N" sort="Zenine, N" uniqKey="Zenine N" first="N." last="Zenine">N. Zenine</name>
<affiliation wicri:level="1"><inist:fA14 i1="03"><s1>Centre de Recherche Nucléaire d'Alger, 2 Bd. Frantz Fanon, BP 399</s1>
<s2>16000 Alger</s2>
<s3>DZA</s3>
<sZ>3 aut.</sZ>
<sZ>7 aut.</sZ>
</inist:fA14>
<country>Algérie</country>
</affiliation>
</author>
</analytic>
<series><title level="j" type="main">Journal of physics. A, Mathematical and theoretical : (Print)</title>
<title level="j" type="abbreviated">J. phys., A, math. theor. : (Print)</title>
<idno type="ISSN">1751-8113</idno>
<imprint><date when="2008">2008</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><title level="j" type="main">Journal of physics. A, Mathematical and theoretical : (Print)</title>
<title level="j" type="abbreviated">J. phys., A, math. theor. : (Print)</title>
<idno type="ISSN">1751-8113</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algorithms</term>
<term>Critical behavior</term>
<term>Differential equations</term>
<term>High temperature</term>
<term>Ising model</term>
<term>Lattice model</term>
<term>Low temperature</term>
<term>Magnetic susceptibility</term>
<term>Power law</term>
<term>Power spectra</term>
<term>Singularity</term>
<term>Spectrum analysis</term>
<term>Square lattices</term>
</keywords>
<keywords scheme="Pascal" xml:lang="fr"><term>Susceptibilité magnétique</term>
<term>Réseau carré</term>
<term>Modèle réticulaire</term>
<term>Modèle Ising</term>
<term>Basse température</term>
<term>Haute température</term>
<term>Algorithme</term>
<term>Equation différentielle</term>
<term>Singularité</term>
<term>Loi puissance</term>
<term>Comportement critique</term>
<term>Spectre puissance</term>
<term>Analyse spectre</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">We calculate very long low- and high-temperature series for the susceptibility X of the square lattice Ising model as well as very long series for the five-particle contribution X<sup>(5)</sup>
 and six-particle contribution X<sup>(6)</sup>
. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150 000 CPU hours on computer clusters. The series for / (low- and high-temperature regimes), X<sup>(5)</sup>
 and X<sup>(6)</sup>
 are now extended to 2000 terms. In addition, for X<sup>(5)</sup>
, 10000 terms of the series are calculated modulo a single prime, and have been used to find the linear ODE satisfied by X<sup>(5)</sup>
 modulo a prime. A diff-Padé analysis of the 2000 terms series for X<sup>(5)</sup>
 and X<sup>(6)</sup>
 confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the n-particle components of the susceptibility, up to a small set of 'additional' singularities. The exponents at all the singularities of the Fuchsian linear ODE of X<sup>(5)</sup>
 and the (as yet unknown) ODE of X<sup>(6)</sup>
 are given: they are all rational numbers. We find the presence of singularities at w = 1/2 for the linear ODE of X<sup>(5)</sup>
, and w<sup>2</sup>
 = 1/8 for the ODE of X<sup>(6)</sup>
, which are not singularities of the 'physical' X<sup>(5)</sup>
 and X<sup>(6)</sup>
, that is to say the series solutions of the ODE's which are analytic at w = 0. Furthermore, analysis of the long series for X<sup>(5)</sup>
 (and X<sup>(6)</sup>
) combined with the corresponding long series for the full susceptibility X yields previously conjectured singularities in some X<sup>(n)</sup>
, n ≥ 7. The exponents at all these singularities are also seen to be rational numbers. We also present a mechanism of resummation of the logarithmic singularities of the X<sup>(n)</sup>
 leading to the known power-law critical behaviour occurring in the full X, and perform a power spectrum analysis giving strong arguments in favour of the existence of a natural boundary for the full susceptibility X.</div>
</front>
</TEI>
<inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>1751-8113</s0>
</fA01>
<fA03 i2="1"><s0>J. phys., A, math. theor. : (Print)</s0>
</fA03>
<fA05><s2>41</s2>
</fA05>
<fA06><s2>45</s2>
</fA06>
<fA08 i1="01" i2="1" l="ENG"><s1>Experimental mathematics on the magnetic susceptibility of the square lattice Ising model</s1>
</fA08>
<fA11 i1="01" i2="1"><s1>BOUKRAA (S.)</s1>
</fA11>
<fA11 i1="02" i2="1"><s1>GUTTMANN (A. J.)</s1>
</fA11>
<fA11 i1="03" i2="1"><s1>HASSANI (S.)</s1>
</fA11>
<fA11 i1="04" i2="1"><s1>JENSEN (I.)</s1>
</fA11>
<fA11 i1="05" i2="1"><s1>MAILLARD (J-M.)</s1>
</fA11>
<fA11 i1="06" i2="1"><s1>NICKEL (B.)</s1>
</fA11>
<fA11 i1="07" i2="1"><s1>ZENINE (N.)</s1>
</fA11>
<fA14 i1="01"><s1>LPTHIRM and Département d'Aéronautique, Université de Blida</s1>
<s3>DZA</s3>
<sZ>1 aut.</sZ>
</fA14>
<fA14 i1="02"><s1>ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne</s1>
<s2>Victoria 3010</s2>
<s3>AUS</s3>
<sZ>2 aut.</sZ>
<sZ>4 aut.</sZ>
</fA14>
<fA14 i1="03"><s1>Centre de Recherche Nucléaire d'Alger, 2 Bd. Frantz Fanon, BP 399</s1>
<s2>16000 Alger</s2>
<s3>DZA</s3>
<sZ>3 aut.</sZ>
<sZ>7 aut.</sZ>
</fA14>
<fA14 i1="04"><s1>LPTMC, Université de Paris, Tour 24, 4ème étage, case 121, 4 Place Jussieu</s1>
<s2>75252 Paris</s2>
<s3>FRA</s3>
<sZ>5 aut.</sZ>
</fA14>
<fA14 i1="05"><s1>Department of Physics, University of Guelph</s1>
<s2>Guelph, Ontario NIG 2W1</s2>
<s3>CAN</s3>
<sZ>6 aut.</sZ>
</fA14>
<fA20><s2>455202.1-455202.51</s2>
</fA20>
<fA21><s1>2008</s1>
</fA21>
<fA23 i1="01"><s0>ENG</s0>
</fA23>
<fA43 i1="01"><s1>INIST</s1>
<s2>577C</s2>
<s5>354000183900970040</s5>
</fA43>
<fA44><s0>0000</s0>
<s1>© 2008 INIST-CNRS. All rights reserved.</s1>
</fA44>
<fA45><s0>33 ref.</s0>
</fA45>
<fA47 i1="01" i2="1"><s0>08-0524292</s0>
</fA47>
<fA60><s1>P</s1>
</fA60>
<fA61><s0>A</s0>
</fA61>
<fA64 i1="01" i2="1"><s0>Journal of physics. A, Mathematical and theoretical : (Print)</s0>
</fA64>
<fA66 i1="01"><s0>GBR</s0>
</fA66>
<fC01 i1="01" l="ENG"><s0>We calculate very long low- and high-temperature series for the susceptibility X of the square lattice Ising model as well as very long series for the five-particle contribution X<sup>(5)</sup>
 and six-particle contribution X<sup>(6)</sup>
. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150 000 CPU hours on computer clusters. The series for / (low- and high-temperature regimes), X<sup>(5)</sup>
 and X<sup>(6)</sup>
 are now extended to 2000 terms. In addition, for X<sup>(5)</sup>
, 10000 terms of the series are calculated modulo a single prime, and have been used to find the linear ODE satisfied by X<sup>(5)</sup>
 modulo a prime. A diff-Padé analysis of the 2000 terms series for X<sup>(5)</sup>
 and X<sup>(6)</sup>
 confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the n-particle components of the susceptibility, up to a small set of 'additional' singularities. The exponents at all the singularities of the Fuchsian linear ODE of X<sup>(5)</sup>
 and the (as yet unknown) ODE of X<sup>(6)</sup>
 are given: they are all rational numbers. We find the presence of singularities at w = 1/2 for the linear ODE of X<sup>(5)</sup>
, and w<sup>2</sup>
 = 1/8 for the ODE of X<sup>(6)</sup>
, which are not singularities of the 'physical' X<sup>(5)</sup>
 and X<sup>(6)</sup>
, that is to say the series solutions of the ODE's which are analytic at w = 0. Furthermore, analysis of the long series for X<sup>(5)</sup>
 (and X<sup>(6)</sup>
) combined with the corresponding long series for the full susceptibility X yields previously conjectured singularities in some X<sup>(n)</sup>
, n ≥ 7. The exponents at all these singularities are also seen to be rational numbers. We also present a mechanism of resummation of the logarithmic singularities of the X<sup>(n)</sup>
 leading to the known power-law critical behaviour occurring in the full X, and perform a power spectrum analysis giving strong arguments in favour of the existence of a natural boundary for the full susceptibility X.</s0>
</fC01>
<fC02 i1="01" i2="3"><s0>001B00</s0>
</fC02>
<fC03 i1="01" i2="3" l="FRE"><s0>Susceptibilité magnétique</s0>
<s5>26</s5>
</fC03>
<fC03 i1="01" i2="3" l="ENG"><s0>Magnetic susceptibility</s0>
<s5>26</s5>
</fC03>
<fC03 i1="02" i2="3" l="FRE"><s0>Réseau carré</s0>
<s5>27</s5>
</fC03>
<fC03 i1="02" i2="3" l="ENG"><s0>Square lattices</s0>
<s5>27</s5>
</fC03>
<fC03 i1="03" i2="X" l="FRE"><s0>Modèle réticulaire</s0>
<s5>28</s5>
</fC03>
<fC03 i1="03" i2="X" l="ENG"><s0>Lattice model</s0>
<s5>28</s5>
</fC03>
<fC03 i1="03" i2="X" l="SPA"><s0>Modelo reticular</s0>
<s5>28</s5>
</fC03>
<fC03 i1="04" i2="3" l="FRE"><s0>Modèle Ising</s0>
<s5>29</s5>
</fC03>
<fC03 i1="04" i2="3" l="ENG"><s0>Ising model</s0>
<s5>29</s5>
</fC03>
<fC03 i1="05" i2="X" l="FRE"><s0>Basse température</s0>
<s5>30</s5>
</fC03>
<fC03 i1="05" i2="X" l="ENG"><s0>Low temperature</s0>
<s5>30</s5>
</fC03>
<fC03 i1="05" i2="X" l="SPA"><s0>Baja temperatura</s0>
<s5>30</s5>
</fC03>
<fC03 i1="06" i2="X" l="FRE"><s0>Haute température</s0>
<s5>31</s5>
</fC03>
<fC03 i1="06" i2="X" l="ENG"><s0>High temperature</s0>
<s5>31</s5>
</fC03>
<fC03 i1="06" i2="X" l="SPA"><s0>Alta temperatura</s0>
<s5>31</s5>
</fC03>
<fC03 i1="07" i2="3" l="FRE"><s0>Algorithme</s0>
<s5>32</s5>
</fC03>
<fC03 i1="07" i2="3" l="ENG"><s0>Algorithms</s0>
<s5>32</s5>
</fC03>
<fC03 i1="08" i2="3" l="FRE"><s0>Equation différentielle</s0>
<s5>33</s5>
</fC03>
<fC03 i1="08" i2="3" l="ENG"><s0>Differential equations</s0>
<s5>33</s5>
</fC03>
<fC03 i1="09" i2="3" l="FRE"><s0>Singularité</s0>
<s5>34</s5>
</fC03>
<fC03 i1="09" i2="3" l="ENG"><s0>Singularity</s0>
<s5>34</s5>
</fC03>
<fC03 i1="10" i2="X" l="FRE"><s0>Loi puissance</s0>
<s5>35</s5>
</fC03>
<fC03 i1="10" i2="X" l="ENG"><s0>Power law</s0>
<s5>35</s5>
</fC03>
<fC03 i1="10" i2="X" l="SPA"><s0>Ley poder</s0>
<s5>35</s5>
</fC03>
<fC03 i1="11" i2="X" l="FRE"><s0>Comportement critique</s0>
<s5>36</s5>
</fC03>
<fC03 i1="11" i2="X" l="ENG"><s0>Critical behavior</s0>
<s5>36</s5>
</fC03>
<fC03 i1="11" i2="X" l="SPA"><s0>Comportamiento crítico</s0>
<s5>36</s5>
</fC03>
<fC03 i1="12" i2="3" l="FRE"><s0>Spectre puissance</s0>
<s5>37</s5>
</fC03>
<fC03 i1="12" i2="3" l="ENG"><s0>Power spectra</s0>
<s5>37</s5>
</fC03>
<fC03 i1="13" i2="X" l="FRE"><s0>Analyse spectre</s0>
<s5>38</s5>
</fC03>
<fC03 i1="13" i2="X" l="ENG"><s0>Spectrum analysis</s0>
<s5>38</s5>
</fC03>
<fC03 i1="13" i2="X" l="SPA"><s0>Análisis espectro</s0>
<s5>38</s5>
</fC03>
<fN21><s1>343</s1>
</fN21>
<fN44 i1="01"><s1>OTO</s1>
</fN44>
<fN82><s1>OTO</s1>
</fN82>
</pA>
</standard>
</inist>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Asie/explor/AustralieFrV1/Data/PascalFrancis/Curation

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 002E60 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/PascalFrancis/Curation/biblio.hfd -nk 002E60 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Asie
   |area=    AustralieFrV1
   |flux=    PascalFrancis
   |étape=   Curation
   |type=    RBID
   |clé=     Pascal:08-0524292
   |texte=   Experimental mathematics on the magnetic susceptibility of the square lattice Ising model
}}

This area was generated with Dilib version V0.6.33.
Data generation: Tue Dec 5 10:43:12 2017. Site generation: Tue Mar 5 14:07:20 2024

	Serveur d'exploration sur les relations entre la France et l'Australie
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur les relations entre la France et l'Australie

Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri