Thermodynamics for spatially inhomogeneous magnetization and Young-Gibbs measures

TL;DR

This paper develops thermodynamic functionals for inhomogeneous magnetization in an Ising model, linking free energy and pressure through a modified Legendre transform, and explores local Gibbs measures via Young-Gibbs measures.

Contribution

It introduces a framework for analyzing spatially inhomogeneous magnetization and constructs Young-Gibbs measures to study local properties of Gibbs states.

Findings

Derived thermodynamic functionals for inhomogeneous magnetization.

Established the relation between free energy and pressure via a modified Legendre transform.

Analyzed local properties of Gibbs measures using Young-Gibbs measures.

Abstract

We derive thermodynamic functionals for spatially inhomogeneous magnetization on a torus in the context of an Ising spin lattice model. We calculate the corresponding free energy and pressure (by applying an appropriate external field using a quadratic Kac potential) and show that they are related via a modified Legendre transform. The local properties of the infinite volume Gibbs measure, related to whether a macroscopic configuration is realized as a homogeneous state or as a mixture of pure states, are also studied by constructing the corresponding Young-Gibbs measures.