A Critical Phenomenon in Solitonic Ising Chains
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss a phase transition of the second order taking place in non-local 1D Ising chains generated by specific infinite soliton solutions of the KdV and BKP equations.
Mots-clés : Ising chain; solitons; phase transition.
@article{SIGMA_2007_3_a58,
     author = {Igor M. Loutsenko and Vyacheslav P. Spiridonov},
     title = {A~Critical {Phenomenon} in {Solitonic} {Ising} {Chains}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2007},
     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a58/}
}
TY  - JOUR
AU  - Igor M. Loutsenko
AU  - Vyacheslav P. Spiridonov
TI  - A Critical Phenomenon in Solitonic Ising Chains
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2007
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a58/
LA  - en
ID  - SIGMA_2007_3_a58
ER  - 
%0 Journal Article
%A Igor M. Loutsenko
%A Vyacheslav P. Spiridonov
%T A Critical Phenomenon in Solitonic Ising Chains
%J Symmetry, integrability and geometry: methods and applications
%D 2007
%V 3
%U http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a58/
%G en
%F SIGMA_2007_3_a58
Igor M. Loutsenko; Vyacheslav P. Spiridonov. A Critical Phenomenon in Solitonic Ising Chains. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a58/

[1] Ablowitz M. J., Segur H., Solitons and the inverse scattering transform, SIAM, Philadelphia, 1981 | MR | Zbl

[2] Andrews G. E., Askey R., Roy R., Special functions, Encyclopedia of Math. Appl., 71, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl

[3] Baxter R. J., Exactly solved models in statistical mechanics, Academic Press, London, 1982 | MR | Zbl

[4] Date E., Jimbo M., Kashiwara M., Miwa T., “Transformation groups for soliton equations”, Nonlinear Integrable Systems, World Scientific, Singapore, 1983, 41–119 | MR

[5] Evans M. R., Phase transitions in one-dimensional nonequilibrium systems, cond-mat/0007293

[6] Gaudin M., “Une famille à une paramètre d'ensembles unitaires”, Nucl. Phys., 85 (1966), 545–575 ; Gaudin M., “Gaz coulombien discret à une dimension”, J. Phys. (France), 34 (1973), 511–522 | DOI | MR

[7] Hirota R., “Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons”, Phys. Rev. Lett., 27 (1971), 1192–1194 | DOI | Zbl

[8] Kuznetsov V. B., “Quadrics on real Riemannian spaces of constant curvature: separation of variables and connection with Gaudin magnet”, J. Math. Phys., 33 (1992), 3240–3254 | DOI | MR | Zbl

[9] Loutsenko I. M., Spiridonov V. P., “Self-similar potentials and Ising models”, Pis'ma v ZhETF (JETP Letters), 66 (1997), 747–753; Loutsenko I. M., Spiridonov V. P., “Spectral self-similarity, one-dimensional Ising chains and random matrices”, Nucl. Phys. B, 538 (1999), 731–758 | DOI | MR | Zbl

[10] Loutsenko I. M., Spiridonov V. P., “Soliton solutions of integrable hierarchies and Coulomb plasmas”, J. Stat. Phys., 99 (2000), 751–767 ; cond-mat/9909308 | DOI | MR | Zbl

[11] Matveev V. B., Salle M. A., Darboux transformations and solitons, Springer Series in Nonlinear Dynamics, Springer-Verlag, 1991 | MR

[12] Spiridonov V. P., “Universal superpositions of coherent states and self-similar potentials”, Phys. Rev. A, 52 (1995), 1909–1935 ; quant-ph/9601030 | DOI

[13] Spiridonov V. P., Zhedanov A. S., “Spectral transformation chains and some new biorthogonal rational functions”, Comm. Math. Phys., 210 (2000), 49–83 | DOI | MR | Zbl