Cluster algorithms

Cluster algorithms for classical and quantum spin systems are discussed. In particular, the cluster algorithm is applied to classical O(N) lattice actions containing interactions of more than two spins. The performance of the multi-cluster and single--cluster methods, and of the standard and improved estimators are compared. (Lecture given at the summer school on `Advances in Computer Simulations', Budapest, July 1996.)Comment: 17 pages, Late

SHAPE OF THE CONSTRAINT EFFECTIVE POTENTIAL - A MONTE-CARLO STUDY

DIMITROVIC I, NAGER J, JANSEN K, Neuhaus T. SHAPE OF THE CONSTRAINT EFFECTIVE POTENTIAL - A MONTE-CARLO STUDY. PHYSICS LETTERS B. 1991;268(3-4):408-414.We compare the shape of the constraint effective potential as obtained from numerical simulations in the scaling limit of the non-linear sigma-model in d = 3 and d = 4 to recent results from chiral perturbation theory. Whereas in d = 4 already the lowest order chiral perturbation theory turns out to describe the data well, we had to use the next to leading order in d = 3 to find satisfactory agreement

Monte Carlo Simulations of Spin Systems

Abstract. This lecture gives a brief introduction to Monte Carlo simulations of classical O(n) spin systems such as the Ising (n = 1), XY (n = 2), and Heisenberg (n = 3) model. In the first part I discuss some aspects of Monte Carlo algorithms to generate the raw data. Here special emphasis is placed on non-local cluster update algorithms which proved to be most efficient for this class of models. The second part is devoted to the data analysis at a continuous phase transition. For the example of the three-dimensional Heisenberg model it is shown how precise estimates of the transition temperature and the critical exponents can be extracted from the raw data. I conclude with a brief overview of recent results from similar high-precision studies of the Ising and XY model.