Convergent perturbation theory for studying phase transitions

M. Yu. Nalimov   ; A. V. Ovsyannikov

Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 2, pp. 226-241

Résumé

We propose a method for constructing a perturbation theory with a finite radius of convergence for a rather wide class of quantum field models traditionally used to describe critical and near-critical behavior in problems in statistical physics. For the proposed convergent series, we use an instanton analysis to find the radius of convergence and also indicate a strategy for calculating their coefficients based on the diagrams in the standard (divergent) perturbation theory. We test the approach in the example of the standard stochastic dynamics $\mathrm A$-model and a matrix model of the phase transition in a system of nonrelativistic fermions, where its application allows explaining the previously observed quasiuniversal behavior of the trajectories of a first-order phase transition.

Détail

Keywords: renormalization group, instanton analysis, superconductivity, critical behavior.
Mots-clés : convergent perturbation theory

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