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 the imaginary fixed points of a $ϕ^3$ theory. Scaling theories and renormalization-group theories are developed to account for the phenomena. Several universality classes with their own hysteresis exponents are found including a field-like thermal class, a partly thermal class, and a purely thermal class, designated respectively as Thermal Class 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 the $ϕ^3$ 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 includes cases in which the order parameters possess different symmetries and thus exhibiting different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only in mean-field level and is identical with Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two-loop results for the static and dynamic exponents for the Yang-Lee edge singularity, which falls into the same universality class to the $ϕ^3$ theory, we estimate the thermal hysteresis exponents of the various classes to the same precisions. Comparisons with numerical results and experiments are briefly discussed.