Universality in two-dimensional magnetic systems

Abstract
Two‐dimensional magnetic behavior in thin films and in layered magnets apparently falls into one of only two universality classes. The first is that of the 2D Ising model, characterized by a magnetization exponent β=1/8. The second, with β≊0.23, is observed in systems with planar spin symmetry. Recently it has been shown, using a modified renormalization group calculation, that β=0.23 is a property of a finite size XY model. Although there is no broken symmetry in this system, correlations below the Kosterlitz–Thouless transition temperature decay so slowly that a magnetization occurs in any realizable system, and β=0.23 is a result of two‐dimensional fluctuations. By considering a large number of experimental situations we demonstrate that this rule is generally obeyed, and can be used as a test to identify two‐dimensional behavior.