Abstract
We simulate 4d SU(N) pure-gauge theories at large N using a parallel tempering scheme that combines simulations with open and periodic boundary conditions, implementing the algorithm originally proposed by Martin Hasenbusch for 2d CPN–1 models. That allows to dramatically suppress the topological freezing suffered from standard local algorithms, reducing the autocorrelation time of Q2 up to two orders of magnitude. Using this algorithm in combination with simulations at non-zero imaginary θ we are able to refine state-of-the-art results for the large-N behavior of the quartic coefficient of the θ-dependence of the vacuum energy b2, reaching an accuracy comparable with that of the large-N limit of the topological susceptibility.
Highlights
While the exact numerical values of the coefficients χ and b2n are generically unknown, something is known about their dependence on the number of colors N, at least when N is large enough
We simulate 4d SU(N ) pure-gauge theories at large N using a parallel tempering scheme that combines simulations with open and periodic boundary conditions, implementing the algorithm originally proposed by Martin Hasenbusch for 2d CP N−1 models
This algorithm was originally tested in two dimensional CP N−1 models, and a first extension of the original proposal has already been performed in ref. [38], by extending the parallel tempering approach to simulations at imaginary θ values
Summary
We discretize the Yang-Mills action on an hyper-cubic lattice of size L and with periodic boundary conditions in every direction (see section 2.3 for the defect) using the standard. We denote by Qccoloovl the topological charge obtained by measuring the observable eq (2.2) on a configuration to which a certain number of cooling steps have been applied. To assign an integer topological charge QL to each configuration we follow ref. That the maxima in the distribution of αQccoloovl are located approximately at integer values; such fixing is performed at θ = 0 and adopted for θ = 0. The topological susceptibility computed using QL becomes stable (i.e. independent of the number of cooling steps ncool) after ncool ∼ 10, such threshold reveals to be weakly dependent on the lattice spacing, we chose ncool = 20 to define the topological charge in all simulations, verifying the stability of all continuum extrapolations if a different value of ncool is used
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