Comparison among HB-inspired algorithms for continuous-spin systems and gauge fields

Abstract

We propose a new local algorithm for the thermalization of n-vector spin models, which can also be used in the numerical simulation of SU(N) lattice gauge theories. The algorithm combines heat-bath (HB) and microcanonical updates in a single step -as opposed to the hybrid overrelaxation method, which alternates between the two kinds of update steps -while preserving ergodicity. We test our proposed algorithm in the case of the one-dimensional 4-vector spin model and compare its performance with the standard HB algorithm and with other HB-inspired algorithms.

Universality in short-time critical gluodynamics with heat-bath-inspired algorithms

“…This may be a hint that effects of some hypothetical ergodicity violations, previously conjectured in[23], would be less harmful than what is expected for some simulations[12] using the OH algorithm.…”

“…We have proposed in [22,23] a modified HB algorithm (MHB) in which the generation of the updating matrix V is carried out as usual, except for the additional step…”

“…Despite being slightly more computer-consuming than OH, our modification implements a micro-canonical move that explicitly preserves ergodicity and allows for a reduction of about 20% in statistical errors, at the same computational cost, when compared with the usual HB algorithm [22,23].…”

“…In this context, we extend our previous comparative study over a class of improved heat-bath-inspired thermalization algorithms [22,23] to the nonequilibrium regime, by using a (2+1)-dimensional SU(2) lattice-gauge theory at critical temperature. It is known that dynamic-relaxation exponents θ and z -namely in contradistinction to static ones: α, β, γ, δ, ν -are generally dependent on the very dynamics of thermalization; so, they would serve as discriminants for algorithmic classes.…”

“…A possible way to circunvent that effect comes from Short-time dynamic techniques [8,10], which enables critical gluodynamics to be efficiently exploited by local [17,18,19] or global [20] updating algorithms. Therefore, to devise improved algorithms [21,22,23] by better understanding their equilibration features -e.g. (over)relaxation dynamics -may be worthy for many applications.…”