Finite size induced phenomena in 2D classical spin models

TL;DR

This paper reviews recent analytic and numerical studies on how finite system size affects the low-temperature phases of 2D XY and Heisenberg models, highlighting phenomena absent in infinite systems.

Contribution

It provides a concise overview of finite size effects on low-temperature properties of 2D classical spin models, emphasizing the emergence of spontaneous magnetization.

Findings

Finite system size induces spontaneous magnetization.

Finite size effects alter low-temperature phase characteristics.

The study clarifies the role of system size in 2D spin models.

Abstract

We make a short overview of the recent analytic and numerical studies of the classical two-dimensional XY and Heisenberg models at low temperatures. Special attention is being paid to an influence of finite system size L on the peculiarities of the low-temperature phase. In accordance with the Mermin-Wagner-Hohenberg theorem, spontaneous magnetisation does not appear in the above models at infinite L. However it emerges for the finite system sizes and leads to new features of the low-temperature behaviour.