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SIGMA 3 (2007), 059, 11 pages arXiv:0704.3173
https://doi.org/10.3842/SIGMA.2007.059
Contribution to the Vadim Kuznetsov Memorial Issue
A Critical Phenomenon in Solitonic Ising Chains
Igor M. Loutsenko a and Vyacheslav P. Spiridonov b
a) Mathematical Institute, University of Oxford, 24-29 St. Gilles',
Oxford, OX1 3LB, UK
b) Bogoliubov Laboratory of Theoretical Physics, JINR,
Dubna, Moscow Region, 141980 Russia
Received December 04, 2006, in final form April 17, 2007; Published online April 24, 2007
Abstract
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.
Key words:
Ising chain; solitons; phase transition.
pdf (215 kb)
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References
- Ablowitz M.J., Segur H., Solitons and the inverse
scattering transform, SIAM, Philadelphia, 1981.
- Andrews G.E., Askey R., Roy R.,
Special functions, Encyclopedia of Math. Appl.,
Vol. 71, Cambridge Univ. Press, Cambridge, 1999.
- Baxter R.J., Exactly solved models in
statistical mechanics, Academic Press, London, 1982.
- Date E., Jimbo M., Kashiwara M., Miwa T.,
Transformation groups for soliton equations, in Nonlinear
Integrable Systems, World Scientific, Singapore, 1983, 41-119.
- Evans M. R., Phase transitions in one-dimensional nonequilibrium
systems, cond-mat/0007293.
- 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.
- Hirota R., Exact solution of the Korteweg-de Vries
equation for multiple collisions of solitons, Phys. Rev. Lett. 27
(1971), 1192-1194.
- 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.
- 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.
- Loutsenko I.M., Spiridonov V.P., Soliton solutions of
integrable hierarchies and Coulomb plasmas, J. Stat. Phys.
99 (2000), 751-767, cond-mat/9909308.
- Matveev V.B., Salle M.A.,
Darboux transformations and solitons,
Springer Series in Nonlinear Dynamics, Springer-Verlag, 1991.
- Spiridonov V.P., Universal superpositions of coherent states
and self-similar potentials, Phys. Rev. A 52 (1995), 1909-1935,
quant-ph/9601030.
- Spiridonov V.P., Zhedanov A.S.,
Spectral transformation chains and some new biorthogonal
rational functions, Comm. Math. Phys. 210 (2000), 49-83.
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