Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing

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.