The phase separation line in the two-dimensional Ising model

Abstract

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Aspects of Ergodic, Qualitative and Statistical Theory of Motion

“…Another example is the proof of the area law for the Wilson loop in a simple lattice gauge theory [GGM78]. One can also mention the microscopic theory of phase coexistence, see [MS67], [GMM73], [Ga72a] and developed in great detail later, see for instance [Mi95]. Problems on large deviations in the theory of Gibbs states can also be solved quite easily by the method, see [GMM78], [GLM02].…”

On the Ising Model with Random Boundary Condition

“…Note that this excludes interfaces in a stronger way than the familiar result about the absence of translationally non-invariant Gibbs measures in the 2d Ising model. (1,22,26) Indeed, the absence of fluctuating interfaces basically means that not only the expectations of local functions but also their space averages (e.g. the volume-averaged magnetization) have only two limit points, corresponding to the two Ising phases.…”

On the Onsager-Yang-Value of the spontaneous magnetization

“…It is known that for/3 large enough ([3 > tic, see Section 1) there are only two translational invariant equilibrium states and it has been announced [13] and partially proven [12] that, for large /3 at least, there are no non-translational invariant equilibrium states (which is a peculiarity of the dimension 2, [-13]).…”