Renormalization-group theory for cooling first-order phase transitions in Potts models

Abstract

We develop a dynamic field-theoretic renormalization-group (RG) theory for the cooling first-order phase transitions in the Potts model. It is suggested that the well-known imaginary fixed points of the $q$-state Potts model for $q>10/3$ in the RG theory are the origin of the dynamic scaling found recently, apart from the logarithmic corrections. This indicates that the real and imaginary fixed points of the Potts model are both physical and control the scalings of the continuous and discontinuous phase transitions, respectively, of the model. Our one-loop results for the scaling exponents are already not far away from the numerical results. Further, the scaling exponents depend on $q$ slightly only, in consistence with the numerical results. Therefore, the theory is believed to provide a natural explanation of the dynamic scaling including the scaling exponents and their scaling laws for various observables in the Potts model.

arXiv comment6 pages, no figure

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• Kinetic Spinodal Instabilities in the Mott Transition in V2O3: Evidence from Hysteresis Scaling and Dissipative Phase Ordering
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Dynamic finite-size scaling at first-order transitions
• Complete universal scaling in first-order phase transitions
• Complex entanglement entropy for complex conformal field theory
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Universal scaling in first-order phase transitions mixed with nucleation and growth
• Observation of heat scaling across a first-order quantum phase transition in a spinor condensate
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Spinodal-like scaling behavior after a temperature quench across the first-order phase transition in three-dimensional $q$-state Potts models