On Limiting Gibbs States of the Two-Dimensional Ising Models

  • Yasunari Higuchi

    Kyoto University, Japan

Abstract

We consider limiting Gibbs states in the two-dimensional ferromagnetic Ising model at sufficiently low temperatures. We prove that every limiting Gibbs state corresponding to a boundary condition such that on every boundary is , where is the number of up-spins on the boundary and is that of down-spins. We also prove that for each , there exists a boundary condition such that on every boundary, and the limiting Gibbs state corresponding to this boundary condition is .

Cite this article

Yasunari Higuchi, On Limiting Gibbs States of the Two-Dimensional Ising Models. Publ. Res. Inst. Math. Sci. 14 (1978), no. 1, pp. 53–69

DOI 10.2977/PRIMS/1195189280