On the Possible Phase Transition for Two-Dimensional Heisenberg Models

Recently the authors presented evidence suggesting the presence of a phase transition for two-dimensional Heisenberg models with nearest-neighbor ferromagnetic interactions and S>½. Here we further analyze the first six coefficients of the high-temperature series for the zero-field susceptibility, and incorporate the results of recent calculations beyond sixth order into the arguments for a phase transition. It is found that the higher-order coefficients support the previous suggestion concerning the existence of a phase transition for S>½, and are consistent with a zero critical temperature for the particular case S=½. Finally, two preliminary calculations on the nature of the low-temperature phase are described. The first of these, due to Dyson, is an intuitive generalization of spin wave theory. The other is an approximate calculation for the rectangular net within the classical Heisenberg model: Considering this net to consist of linear chains, the intrachain interactions are treated exactly, while the interchain interactions are treated via a molecular field approximation. Both of these calculations support the original suggestion of a phase transition for two-dimensional Heisenberg models.