Isotropic magnets in two dimensions

Abstract

The authors have re-examined the high-temperature susceptibility series (through tenth order) for the classical isotropic n=2 (X-Y and planar Heisenberg) and n=3 (Heisenberg) models, following suggestions by Kosterlitz and Thouless (see abstr. A36398 of 1973) that the (n=2) phase transition may be understood in terms of 'topological' order in a dilute vortex gas. Evidence is found (most conclusive for n=2, X-Y) supporting Kosterlitz' suggestion (see abstr. A41169 of 1974) that the susceptibility behaves as X₀ exp(A epsilon ^{- nu} ), where epsilon =1-K/K_c. For the X-Y case, the authors obtain an apparent exponent of nu approximately=0.75-0.77. For the planar and (n=3) Heisenberg models the evidence is weaker but indicative of nu approximately=0.7 in the former case and nu approximately=0.8 in the latter.