The critical behaviour of two-dimensional isotropic spin systems

Abstract

The high-temperature susceptibility and internal energy series have been reexamined for four two-dimensional isotropic spin models on a triangular lattice. They are the planar classical Heisenberg (PCH), infinite spin X-Y, classical Heisenberg and step models. For all four models evidence of a phase transition is found. This evidence is good for the first two models, and weak for the last two. A method of series analysis is developed which permits us to rule out, with some degree of confidence, an algebraic singularity for either the susceptibility or the specific heat for all four models. For the PCH model the susceptibility fits the form suggested by Kosterlitz (1974) while for the X-Y model susceptibility a similar conclusion may be drawn, with a lesser degree of confidence.