Renormalization group theory for temperature-driven first-order phase transitions in scalar models

Abstract

We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ³ theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found: a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ³ theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and twoloop results for the static and dynamic exponents for the Yang–Lee edge singularity, respectively, which falls into the same universality class as φ³ theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.

Keywords

first-order phase transitions / thermal phase transitions / renormalization group theory / φ³ theory / scaling and universality / thermal classes / instability exponents / finite-time scaling / scalar model / dynamics / thermal hysteresis

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