Instability of Phase Coexistence and Translation Invariance in Two Dimensions

Abstract

All the equilibrium states of the two-dimensional Ising system are convex combinations of the pure phases and, as such, translation invariant. This has been rigorously proven and is related to the instability of phase boundary lines with respect to thermal fluctuations. While in higher dimensions stable phase coexistence is known to occur, the instability is expected to be typical of two-dimensional systems.