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 N+/N– < θ < 3/5 on every boundary is μ–, where N+ is the number of up-spins on the boundary and N– is that of down-spins. We also prove that for each θ > 3/5, there exists a boundary condition such that 3/5 < N+/N– ≤ θ on every boundary, and the limiting Gibbs state corresponding to this boundary condition is μ+.
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. 53–69DOI 10.2977/PRIMS/1195189280