Jarzynski’s theorem for lattice gauge theory

Abstract

Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.

Excluded-volume effects for a hadron gas in Yang-Mills theory

“…We compute all expectation values of physical quantities by Monte Carlo integration, using ensembles of configurations produced by an algorithm combining heat-bath [40] and over-relaxation updates [41], and estimate the statistical uncertainties of our simulation results by the jackknife method [42]. We set the physical scale of our lattice simulations using the string tension σ (in lattice units) extracted from the zero-temperature static quark-antiquark potential: for 2.25 ≤ β ≤ 2.6, the values of σa 2 for this theory can be interpolated by [43] …”

QCD in a moving frame: an exploratory study

“…Following some of these strategies promising results for the EoS have already been obtained, both in SU(3) Yang-Mills theory and QCD [45,46]. From a different perspective, other promising ideas for determining the EoS have been devised and tested [47,48].…”

Conformal perturbation theory confronts lattice results in the vicinity of a critical point

“…The calculation of off-critical correlators by means of CPT has greatly benefited from the recent progress in the determination of universal quantities by the conformal-bootstrap method (see ref. [39] for a recent review): in particular, accurate predictions have been worked out for the perturbations of conformal models in the universality class of the three-dimensional Ising model [7,8].…”

“…(6) and (7) of ref. [8], ∂ t C σσ1 (0, r) can be computed by a Mellin transform, and reduced to a combination of Euler integrals of the second kind, which are functions of ∆ . Note that eq.…”

“…While its original application was limited to two-dimensional models, see for example refs. [2][3][4][5][6], recently it has also been extended to theories defined in three dimensions [7,8], thanks to the recent developments in the calculation of Wilson coefficients using the conformal bootstrap approach [9,10].…”