G. N. J. Ananos | Searcharxiv

arXiv2001

The Effective Potential for Composite Operator in the Scalar Model at Finite Temperature

We discuss the $ϕ^4$ and $ϕ^6$ theory defined in a flat $D$-dimensional space-time. We assume that the system is in equilibrium with a thermal bath at temperature $β^{-1}$. To obtain non-perturbative result, the $ 1/N $ expansion is used. The method of the composite operator (CJT) for summing a large set of Feynman graphs, is developed for the finite temperature system. The ressumed effective potential and the analysis of the D=3 and D=4 cases are given.

hep-th↗

arXiv1997

Dimensional reduction of the chiral-continous Gross-Neveu model

We study the finite-temperature phase transition of the generalized Gross-Neveu model with continous chiral symmetry in $2 < d \leq 4$ euclidean dimensions. The critical exponents are computed to the leading order in the $1/N$ expansion at both zero and finite temperatures. A dimensionally reduced theory is obtained after the introduction of thermal counterterms necessary to cancel thermal divergences that arise in the limit of high temperature. Although at zero temperature we have an infinitely and continously degenerate vacuum state, we show that at finite temperature this degeneracy is discrete and, depending on the values of the bare parameters, we may have either total or partial restoration of symmetry. Finally we determine the universality class of the reduced theory by a simple analysis of the infrared structure of thermodynamic quantities computed using the reduced action as starting point.

hep-th↗