Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group

Abstract

We apply to the calculation of the pressure of a hot scalar field theory a method that has been recently developed to solve the Non-Perturbative Renormalization Group. This method yields an accurate determination of the momentum dependence of n-point functions over the entire momentum range, from the low momentum, possibly critical, region up to the perturbative, high momentum region. It has therefore the potential to account well for the contributions of modes of all wavelengths to the thermodynamical functions, as well as for the effects of the mixing of quasiparticles with multi-particle states. We compare the thermodynamical functions obtained with this method to those of the so-called Local Potential Approximation, and we find extremely small corrections. This result points to the robustness of the quasiparticle picture in this system. It also demonstrates the stability of the overall approximation scheme, and this up to the largest values of the coupling constant that can be used in a scalar theory in 3+1 dimensions. This is in sharp contrast to perturbation theory which shows no sign of convergence, up to the highest orders that have been recently calculated.

Massive renormalization scheme and perturbation theory at finite temperature

“…[8,10]), and indeed, as we have already emphasized, the main properties of the present renormalization scheme are automatically included in such an approach. Note that the calculations presented in Fig.…”

“…resummations, the use of functional variational techniques such as the so-called 2PI (two particle irreducible) formalism [7], or the non-perturbative renormalization group (NPRG) [8]. Remarkably, all these approaches produce results that remain stable as one increases the coupling constant, in sharp contrast with strict perturbation theory.…”

“…At the same time, some of these calculations suggest that the physics at moderate coupling is minimally non-perturbative. In particular, calculations using the functional renormalization group within the most sophisticated approximation scheme available [8,9] yield results that do not deviate much from simple self-consistent quasiparticle approximations (such as the lowest order 2PI approximation, or the local potential approximation of the NPRG [10]). …”

Asymptotically free theory with scale invariant thermodynamics

“…27) where I 1 is the (Euclidean) one-loop integral given by Eq. (3.8) in MS renormalization scheme, with the thermal part J 1 (x) having the high-T expansion(5.18).…”

Scale-Invariant Resummed Perturbation at Finite Temperatures

“…Accordingly the predictions are, a priori, less convergent than for the T = 0 case. A plethora of nonperturbative approximations attempting to resum thermal perturbative expansions have been developed and refined over the years [1,[4][5][6]. The so-called optimized perturbation theory (OPT) is a variational approach in which a related solvable case is rewritten in terms of an unphysical parameter, allowing for optimized nonperturbative results.…”