Monte Carlo study of tricritical dynamics in two dimensions

Tyler Cary, Richard T. Scalettar, Rajiv R. P. Singh

David Paul Landau, Robert H. Swendsen

Using a Monte Carlo renormalization-group (MCRG) method we study tricritical behavior in two very different two-dimensional spin models: the Blume-Capel ferromagnet and the next-nearest-neighbor Ising antiferromagnet. The MCRG method is used to locate accurately tricritical points independent of the convergence of eigenvalue estimates. Despite the different symmetries and the different renormalization transformations used for the two models, in both cases we find four relevant tricritical eigenvalues which are essentially identical for both models. For the antiferromagnet, there is no indication of any decomposition of the tricritical point as predicted by mean-field theory, for ratios of intrasublattice to intersublattice coupling as small as (1/8).

David Paul Landau

David Paul Landau

David Paul Landau, Robert H. Swendsen

A powerful, new extension of the Monte Carlo renormalization-group (MCRG) method is used to accurately determine the tricritical point and exponents in two very different two-dimensional models: an Ising antiferromagnet and a Blume-Capel model. We find four relevant tricritical eigenvalues which are essentially identical for both models. We also demonstrate that subtle warning signals appear in a standard Monte Carlo calculation when a second-order transition is being misinterpreted as first order.

Eytan Domany, James E. Gubernatis

Critical dynamics in d dimensions can be mapped onto a supersymmetric equilibrium problem in d+1 with a Lifshitz tricritical point. The existence of such a point is demonstrated for the Ising model on the hcp lattice by Monte Carlo simulation.