3 research outputs found
Phase transitions in self-dual generalizations of the Baxter-Wu model
We study two types of generalized Baxter-Wu models, by means of
transfer-matrix and Monte Carlo techniques. The first generalization allows for
different couplings in the up- and down triangles, and the second
generalization is to a -state spin model with three-spin interactions. Both
generalizations lead to self-dual models, so that the probable locations of the
phase transitions follow. Our numerical analysis confirms that phase
transitions occur at the self-dual points. For both generalizations of the
Baxter-Wu model, the phase transitions appear to be discontinuous.Comment: 29 pages, 13 figure
Monte Carlo investigations of phase transitions: status and perspectives
Using the concept of finite-size scaling, Monte Carlo calculations of various
models have become a very useful tool for the study of critical phenomena, with
the system linear dimension as a variable. As an example, several recent
studies of Ising models are discussed, as well as the extension to models of
polymer mixtures and solutions. It is shown that using appropriate cluster
algorithms, even the scaling functions describing the crossover from the Ising
universality class to the mean-field behavior with increasing interaction range
can be described. Additionally, the issue of finite-size scaling in Ising
models above the marginal dimension (d*=4) is discussed.Comment: 23 pages, including 14 PostScript figures. Presented at
StatPhys-Taiwan, August 9-16, 1999. Also available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm