Thermodynamics for spatially inhomogeneous magnetization and Young-Gibbs measures

Research paper by A. Montino, N. Soprano-Loto, D. Tsagkarogiannis

Indexed on: 23 May '16Published on: 23 May '16Published in: Mathematics - Probability


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.