Salas, Jesus
Title: Dynamic critical behavior of the Wang-Swendsen-Kotecky algorithm for two-dimensional Potts antiferromagnets
Author: Jesus Salas
Affiliation: Universidad Carlos III de Madrid, Spain
Abstract:
The phase diagram of the antiferromagnetic q-state Potts model is not universal: it depends, in addition to the number of states q and the dimensionality of the lattice, on the lattice structure. Therefore, one has to study this model on a case-by-case basis. For q large enough, the system is always disordered, even at zero temperature (T=0), and in some cases, there are also critical points at T=0. Monte Carlo simulations provide a fruitful way to investigate this phase diagram, and the (non-local) Wang-Swendsen-Kotecky (WSK) dynamics is one of the algorithms of choice for such simulations. (For non-frustrated systems, WSK contains single-site moves as a particular case.)
In this talk, we briefly review the main properties of the WSK algorithm. For bipartite lattices, it can be proven that WSK satisfies all the required properties to converge to the right probability distribution. For q=3, we provide several examples (on the square, hexagonal, and diced lattices) that demonstrate that the dynamic critical behavior of WSK also depends strongly on the lattice structure of the model. For non-bipartite lattices, we show that the WSK algorithm for the q=4 model on the triangular lattice and the closely related q=3 model on the kagome lattice are non-ergodic at T=0. (This also implies that single-site dynamics is non-ergodic at T=0.) Therefore, new Monte Carlo algorithms are needed for such systems.
Author: Jesus Salas
Affiliation: Universidad Carlos III de Madrid, Spain
Abstract:
The phase diagram of the antiferromagnetic q-state Potts model is not universal: it depends, in addition to the number of states q and the dimensionality of the lattice, on the lattice structure. Therefore, one has to study this model on a case-by-case basis. For q large enough, the system is always disordered, even at zero temperature (T=0), and in some cases, there are also critical points at T=0. Monte Carlo simulations provide a fruitful way to investigate this phase diagram, and the (non-local) Wang-Swendsen-Kotecky (WSK) dynamics is one of the algorithms of choice for such simulations. (For non-frustrated systems, WSK contains single-site moves as a particular case.)
In this talk, we briefly review the main properties of the WSK algorithm. For bipartite lattices, it can be proven that WSK satisfies all the required properties to converge to the right probability distribution. For q=3, we provide several examples (on the square, hexagonal, and diced lattices) that demonstrate that the dynamic critical behavior of WSK also depends strongly on the lattice structure of the model. For non-bipartite lattices, we show that the WSK algorithm for the q=4 model on the triangular lattice and the closely related q=3 model on the kagome lattice are non-ergodic at T=0. (This also implies that single-site dynamics is non-ergodic at T=0.) Therefore, new Monte Carlo algorithms are needed for such systems.