Fixed Points and Crossovers for the Hysteresis Scaling of Dynamic Mean-Field Models

Abstract Phase transitions are divided into first-order and continuous ones in the current classification. While the latter shows striking phenomena of scaling and universality, the former is typically characterized by discontinuous jumps in extensive variables and pronounced hysteresis. Recent studies have demonstrated universal scaling behavior controlled by a cubic fixed point in first-order phase transitions. However, more recent investigations of hysteresis in a dynamic mean-field quartic model driven across its first-order phase transitions have revealed new scaling exponents for different driving rates. Here, we discover a new exponent for large driving rates arising surprisingly from critical phenomena and show that, depending on the magnitude of the driving rates and the absence or presence of noise, the same mean-field model remarkably exhibits several universality classes with definite universal scaling exponents governed by their corresponding fixed points, as revealed through a systematic scaling analysis based on renormalization group theory. The theories, the various crossovers between different fixed points, and the complete universal scaling of full curve collapse, are all verified by numerical results. This further confirms universal scaling in first-order phase transitions.