Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions

TL;DR

This paper proves the existence of a shape-dependent thermodynamic limit in spin systems with short- and long-range interactions, highlighting the nonadditivity of thermodynamic functions due to system shape.

Contribution

It establishes the shape-dependent thermodynamic limit and derives variational expressions for entropy and free energy densities in spin systems.

Findings

Thermodynamic limit exists with fixed system shape.

Thermodynamic functions depend explicitly on system shape.

Nonadditivity is confirmed as a key feature of long-range interactions.

Abstract

The existence of the thermodynamic limit in spin systems with short- and long-range interactions is established. We consider the infinite-volume limit with a fixed shape of the system. The variational expressions of the entropy density and the free energy density are obtained, which explicitly depend on the shape of the system. This shape dependence of thermodynamic functions implies the nonadditivity, which is one of the most important characteristics of long-range interacting systems.