The Schonmann projection as a g-measure-, how Gibbsian is it?

TL;DR

This paper investigates the Schonmann projection of the 2D Ising model's Gibbs measures, showing it is a g-measure with continuous one-sided boundary condition dependence despite being non-Gibbsian at low temperatures.

Contribution

It proves that the Schonmann projection, previously known to be non-Gibbsian, is actually a g-measure with continuous one-sided boundary dependence.

Findings

Schonmann projection is a g-measure.

Conditional probabilities depend continuously on one-sided boundary conditions.

The measure is non-Gibbsian due to discontinuity in two-sided boundary conditions.

Abstract

We study the one-dimensional projection of the extremal Gibbs measures of the two-dimensional Ising model, the "Schonmann projection". These measures are known to be non-Gibbsian at low temperatures, since their conditional probabilities as a function of the two-sided boundary conditions are not continuous. We prove that they are g-measures, which means that their conditional probabilities have a continuous dependence on one-sided boundary condition.