The Problem of Confluent Singularities

Gustavo A. Arteca, Francisco Marcelo Fernández, Eduardo Alberto Castro

Svend J. Knak Jensen, Ole G. Mouritsen

The singularity of the heat capacity for the spin- 1 / 2 Ising ferromagnet arrayed on simple cubic and diamond lattices is investigated through the analysis of high-precision Monte Carlo data for the internal energy. The analysis incorporates confluent singularities. Two least-squares fitting procedures are considered. In the first one, the leading confluent singularity amplitude is zero and the next confluent singularity is included. For both lattices this procedure gives accordance with: (i) the universal value for the ratio of the leading singularity amplitudes predicted from the epsilon expansion and (ii) the theoretical expectation of equality between the non-singular parts of the heat capacity above and below the critical temperature. In the second least-squares fitting procedure, the leading confluent singularity is finite. This leads to a fit which disagrees with both (i) and (ii). The Monte Carlo results suggest that the failure of the series analysis to accord with (i) and (ii) may be due to neglect of a rather large confluent singularity in the ferromagnetic phase.

Yves Pomeau A, Minh-Binh Tran

Gusein Sh. Guseinov

John J. Rehr

Using a confluent singularity analysis based on the generalised recurrence method, the series for the correlation length in terms of a dimensionless coupling constant is analysed, extending an approach of Nickel and Sharpe (1979). The results suggest that the spin- 1 / 2 BCC Ising model satisfies hyperscaling and has the same confluent singularity structure expected for models of the (n=1, D=3) universality class.

Martin Gebert, Heinrich Küttler, Peter Müller