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.

23 pages, 9 figures

References in corpus (5)

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• Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature
• Four-loop screened perturbation theory
• Pressure to order $g^8\ast log(g)$ in ${\varphi }^4$-theory at weak coupling
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• Asymptotically Free Theory with Scale Invariant Thermodynamics
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• Renormalization group optimized $\lambda {\varphi }^4$ pressure at next-to-next-to-leading order
• Time Evolution and Thermal Renormalization Group Flow in Cosmology
• Pressure of massless hot scalar theory in the boundary effective theory framework
• Thermal and Quantum Phase Transitions of the ${\varphi }^4$ Model
• Scale dependence improvement of the quartic scalar field thermal effective potential in the optimized perturbation theory