Abstract
We study the coexistence phase in the two-dimensional Ising model. Optimizing the cluster expansion technique, we are able to prove the phase separation phenomenon, with the Onsager value for the surface tension, in a range\(\beta > \bar \beta\), where\(\bar \beta\) estimates from above the critical β within 19% and essentially coincides with the entropic bound.
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References
A. Messager and S. Miracle-Sole, Equilibrium states of the two dimensional Ising model in the two phase region,Commun. Math. Phys. 40:187–196 (1975).
L. Onsager, Crystal statistics. I. A two dimensional model with an order-disorder transition,Phys. Rev. 65:117 (1944)
G. Gallavotti, A. Martin-Löf, and S. Miracle-Solé, Some problems connected with the description of coexisting phases at low temperatures in the Ising model, inStatistical Mechanics and Mathematical Problems, A. Lenard, ed. (Springer-Verlag, New York, 1973).
E. Olivieri, On a cluster expansion for lattice spin system: A finite-size condition for the convergence,Stat. Phys. 50(5/6):1179–1200 (1988).
R. Kotecky and D. Preiss, Cluster expansion for abstract polymer models,Commun. Math. Phys. 103:491–498 (1986).
R. L. Dobrushin, Estimates of semiinvariants for the Ising model at low temperatures, ESI preprint 125 (1994).
C. Gruber and H. Kunz, General properties of polymer system,Commun. Math. Phys. 22:133–161 (1971).
D. Ruelle,Statistical Mechanics (Benjamin, New York, (1987).
C. Gruber, A. Hintermann, A. Messager, and S. Miracle-Sole, On the uniqueness of the invariant equilibrium state and surface tension,Commun. Math. Phys. 56:147–159 (1977).
D. Ioffe, Large deviations for the 2D ising model: A lower bound without cluster expansion,J. Stat. Phys., to appear.
D. B. Abraham, Surface structure and phase transition, inPhase Transition and Critical Phenomena, Vol. 10, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1987).
H. van Beijeren and G. Gallavotti, The phase separation line in the two-dimensional Ising model and its relationship with the nonfree-random-walk problem,Lett. Nuovo Cimento 14:699–703 (1972).
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Communicated by F. Martinelli
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Contucci, P. An analyticity bound for two-dimensional Ising model at low temperature. J Stat Phys 82, 1647–1657 (1996). https://doi.org/10.1007/BF02183397
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DOI: https://doi.org/10.1007/BF02183397