Finite size induced phenomena in 2D classical 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.