Abstract
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.
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This research was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASISтАЭ (Grant No. 19-1-1-35-1).
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Nalimov, M.Y., Ovsyannikov, A.V. Convergent perturbation theory for studying phase transitions. Theor Math Phys 204, 1033–1045 (2020). https://doi.org/10.1134/S004057792008005X
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DOI: https://doi.org/10.1134/S004057792008005X