Geodesic
Convergent perturbation theory for studying phase transitions
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 2, pp. 226-241

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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.
Keywords: renormalization group, instanton analysis, convergent perturbation theory, superconductivity, critical behavior. 
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     author = {M. Yu. Nalimov and A. V. Ovsyannikov},
     title = {Convergent perturbation theory for studying phase transitions},
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M. Yu. Nalimov; A. V. Ovsyannikov. Convergent perturbation theory for studying phase transitions. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 2, pp. 226-241. http://geodesic.mathdoc.fr/item/TMF_2020_204_2_a4/