# 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 *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+.