Nonlocal Monte Carlo algorithms for statistical physics applications

Abstract

After a brief general overview of Monte Carlo computer simulations in statistical physics, special emphasis is placed on applications to phase transitions and critical phenomena. Here, standard simulations employing local update algorithms are severely hampered by the problem of critical slowing down, that is by strong correlations between successively generated data. It is shown that this problem can be greatly reduced by using nonlocal update techniques such as cluster and multigrid algorithms. The general ideas are illustrated for simple lattice spin models and Euclidean path integrals. # 1998 IMACS/ Elsevier Science B.V.

Vortex-line percolation in the three-dimensional complex∣ψ∣4model

“…11 The modulus of ψ is updated with a Metropolis algorithm. 15,16 Here some care is necessary to treat the measure in Eq. (4) properly (see Ref.…”

Introduction to Simulation Techniques

“…Soon after Wolff [89] discovered the so-called single-cluster variant and developed a generalization to O(n)-symmetric spin models. By now cluster updates have been derived for many other models as well [90], but they are still less general applicable than local update algorithms of the Metropolis type. We therefore start again with the Ising model where (as for more general Potts models) the prescription for a cluster-update algorithm can be easily read off from the equivalent Fortuin-Kasteleyn representation [91][92][93][94],…”

Dynamic critical behavior of the Swendsen?Wang algorithm for the three-dimensional Ising model

“…β Potts = 0.44330918), which is Blöte et al's [39] best estimate of the critical temperature and is very near to the estimates by other workers [40,41] (see also the review [42]). We studied lattice sizes L = 4, 6,8,12,16,24,32,48,64,96,128,192,256 and performed between 2.9 × 10 7 and 5 × 10 8 SW iterations for each lattice size (see Table 1). The total data set at each L corresponds to ≈ 10 6 τ on the largest lattices (L = 192, 256), at least 10 7 τ on all L ≤ 64, and nearly 10 8 τ at L = 16 (see again Table 1).…”

“…Recall that exponential autocorrelation time of an observable O is defined as 8) and that the exponential autocorrelation time of the system is defined as…”