Related papers: Cluster representations and the Wolff algorithm in…
Monte Carlo simulation using a cluster algorithm is used to compute the scaling part of the free energy for a three dimensional O(4) spin model. The results are relevant for analysis of lattice studies of high temperature QCD.
A new algorithm for simulating compact U(1) lattice gauge theory in three dimensions is presented which is based on global changes in the configuration space. We show that this algorithm provides an effective way to extract partition…
We present cluster Monte Carlo algorithms for the $XYZ$ quantum spin models. In the special case of $S=1/2$, the new algorithm can be viewed as a cluster algorithm for the 8-vertex model. As an example, we study the $S=1/2$ $XY$ model in…
We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and…
This work is concerned with the theory of Graphical Representation for the Ising and Potts Models over general lattices with non-translation invariant external field. We explicitly describe in terms of the Random Cluster Representation the…
We present an optimized version of a cluster labeling algorithm previously introduced by the authors. This algorithm is well suited for large-scale Monte Carlo simulations of spin models using cluster dynamics on parallel computers with…
We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm,…
We present a new type of cluster algorithm that strongly reduces critical slowing down in simulations of vertex models. Since the clusters are closed paths of bonds, we call it the {\em loop algorithm}. The basic steps in constructing a…
Two cluster algorithms, based on constructing and flipping loops, are presented for worldline quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip…
We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its…
Despite their formal simplicity, most lattice spin models cannot be easily solved, even under the simplifying assumptions of mean field theory. In this manuscript, we present a method for generating mean field solutions to classical…
Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are…
Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are…
The theory of spin models intersects with condensed matter physics, complex systems, graph theory, combinatorial optimization, computational complexity and neural networks. Many ensuing applications rely on the fact that complicated spin…
We present a general strategy to extend quantum cluster algorithms for S=1/2 spin systems, such as the loop algorithm, to systems with arbitrary size of spins. In general, the partition function of a high-S spin system is represented in…
Auxiliary field quantum Monte Carlo methods for Hubbard models are generally based on a Hubbard-Stratonovitch transformation where the field couples to the z-component of the spin. This transformation breaks SU(2) spin invariance. The…
We have developed an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with…
Cluster molecular field approximations represent a substantial progress over the simple Weiss theory where only one spin is considered in the molecular field resulting from all the other spins. In this work we discuss a systematic way of…
Despite several attempts, no efficient cluster algorithm has been constructed for CP(N-1) models in the standard Wilson formulation of lattice field theory. In fact, there is a no-go theorem that prevents the construction of an efficient…
The behaviour of the 3D axial next-nearest neighbour Ising (ANNNI) model at the uniaxial Lifshitz point is studied using Monte Carlo techniques. A new variant of the Wolff cluster algorithm permits the analysis of systems far larger than in…