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.

中文翻译：

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收敛微扰理论用于研究相变

摘要

我们提出了一种用于构造一类具有有限会聚半径的扰动理论的方法，该方法用于相当广泛的一类量子场模型，这些模型通常用于描述统计物理问题中的临界和近临界行为。对于拟议的收敛级数，我们使用实例分析来找到收敛半径，并指出一种基于标准（发散）扰动理论中的图计算其系数的策略。我们在标准随机动力学\（\ mathrm {A} \）模型和非相对论费米子系统中的相变矩阵模型的示例中测试了该方法，在此方法中的应用可以解释以前观测到的准相对论行为。一阶相变的轨迹。