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

TL;DR

This paper develops a renormalization-group theory to explain the dynamic scaling behavior observed during cooling first-order phase transitions in the Potts model, linking fixed points to physical phenomena.

Contribution

It introduces a dynamic RG framework that accounts for both real and imaginary fixed points, explaining scaling laws in Potts models with different q values.

Findings

Imaginary fixed points are linked to dynamic scaling in first-order transitions.

Scaling exponents depend weakly on q, consistent with numerical data.

The theory explains observed scaling laws and exponents 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.