Strong coupling from non-equilibrium Monte Carlo simulations

Abstract

We compute the running coupling of non-Abelian gauge theories in the Schrödinger-functional scheme, by means of non-equilibrium Monte Carlo simulations on the lattice.

Calculation of the running coupling in non-Abelian gauge theories from Jarzynski's equality

“…As detailed in ref. [1], our non-equilibrium algorithm proves computationally very efficient, and we expect that it may reveal its full power especially in situations where standard Monte Carlo calculations are hampered by particularly challenging computational complexity problems. Finally, while the present study was carried out in purely gluonic theories, the extension to full QCD is straightforward, and the generalization to a diverse array of other physical quantities is possible.…”

“…As an example, in this presentation we discussed the study reported in ref. [1], in which Jarzynski's equality was used to compute the quantum effective action in the Schrödinger-functional formalism, from which one can determine the running coupling in this scheme. Our results for SU(2) and SU(3) Yang-Mills theories are fully for SU(2) Yang-Mills theory and perturbative predictions at one (dashed black curve), two (dash-dotted black line), and three loops (dotted black curve), according to eq.…”

“…In this contribution we discuss our recent work [1], presenting an application of a new type of non-equilibrium Monte Carlo algorithms for lattice field theory. The formalism underlying our work rests on some theorems that were formulated in non-equilibrium statistical mechanics during the 1990's [2][3][4][5][6][7] which, in addition to giving new mathematical insights into irreversibility and non-equilibrium phenomena, also provide the basis for a novel type of Monte Carlo calculations.…”

Monopole-like configurations in the O(3) spin model at the upper critical dimension

“…Future studies on this model might include investigating the system in an out-of-equilibrium setting, as already explored in [21], which would allow us to study the non-equilibrium dynamics of the monopole excitation.…”

Stochastic normalizing flows as non-equilibrium transformations

“…A different computational strategy to evaluate free-energy or effective-action differences has been recently pursued in a series of works [8][9][10][11][12] that are based on an exact equality in nonequilibrium statistical mechanics discovered by C. Jarzynski more than 25 years ago [13]. It expresses the free-energy difference between two equilibrium states of a statistical system in terms of the exponential average of the work done on the system to push it out of equilibrium.…”