Curvature of the QCD phase transition line in a finite volume

Abstract

The curvature which characterizes the QCD phase transition at finite temperature and small values of the chemical potential is accessible to lattice simulations. The results for this quantity which have been obtained by several different lattice simulation methods differ due to different numbers of flavors, different pion masses and different sizes of the simulation volume. In order to reconcile these results, it is important to investigate finite-volume effects on the curvature.We investigate the curvature of the chiral phase transition line at finite temperature and chemical potential in a finite volume. We use a phenomenological model for chiral symmetry breaking and apply non-perturbative functional renormalization group methods which account for critical long-range fluctuations at the phase transition.We find an intermediate volume region in which the curvature of the phase transition line is actually reduced relative to its infinite-volume value, provided periodic spatial boundary conditions are chosen for the quark fields. Size and location of this region depend on the value of the pion mass. Such an effect could account for differences in the curvature between lattice simulations in differently sized volumes and from functional methods in the infinite volume limit. We discuss implications of our results for the QCD phase diagram.

Fermion interactions and universal behavior in strongly interacting theories

“…Let us assume for the moment that it would be possible to integrate out the gauge degrees of freedom completely. The dynamics associated with the gauge fields would then be encoded in highly non-local fermionic self-interactions of arbitrarily high order 56 . We assume further that the strength of these dynamically generated fermionic self-interactions can be related to a set of initial conditions for this purely fermionic theory at a given (UV) scale H by means of an RG trajectory.…”

“…In any case, it is well known that the mass spectrum and the thermodynamics of QCD has an intriguing dependence on the volume size and the boundary conditions of the fields, see e.g. [46][47][48][49][50][51][52][53][54][55][56][57].…”

Finite-Volume Effects in Quantum Chromodynamics and Functional Renormalization Group Methods

“…We then use a non-perturbative RG equation [1] to investigate the dynamically generated chiral symmetry breaking and to take all relevant fluctuations into account. Including explicit symmetry breaking, this approach is directly applicable to finite volume as well [12,24,27,[29][30][31][32]. Chiral symmetry breaking in the model is realized through a non-zero expectation value σ 0 = σ ∼ ψ ψ for one of the fields.…”