Phase Transitions in Continuum Ferromagnets with Unbounded Spins

TL;DR

This paper investigates phase transitions in an infinite continuum ferromagnetic system with unbounded spins, demonstrating the existence of multiple thermodynamic states under high activity conditions.

Contribution

It establishes the existence of multiple Gibbs measures for continuum ferromagnets with unbounded spins, under certain interaction and activity conditions.

Findings

Multiple Gibbs measures exist at high activity levels.

The system exhibits phase transitions with unbounded spin interactions.

Attractive finite-range spin interactions lead to multiple equilibrium states.

Abstract

States of thermal equilibrium of an infinite system of interacting particles in a Euclidean space are studied. The particles bear 'unbounded' spins with a given symmetric a priori distribution. The interaction between the particles is pairwise and splits into position-position and spin-spin parts. The position-position part is described by a superstable potential, and the spin-spin part is attractive and of finite range. Thermodynamic states of the system are defined as tempered Gibbs measures on the space of marked configurations. It is proved that the set of such measures contains at least two elements if the activity is big enough.