Renormalization-group theory of first-order phase transition dynamics in field-driven scalar model

Abstract

Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ³ theory, we show that the instability fixed points of the theory, together with their associated instability exponents, are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar φ⁴ model, below its critical temperature and near the instability points. Finitetime scaling and leading corrections to the scaling are considered. We also show that the instability exponents of the first-order phase transitions are equivalent to those of the Yang–Lee edge singularity, and employ the latter to improve our estimates of the former. The outcomes agree well with existing numerical results.

Keywords

first-order phase transitions / renormalization group theory / φ³ theory / scaling and universality / instability exponents / Yang–Lee edge singularity / finite-time scaling / corrections to scaling / scalar model / dynamics / hysteresis

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