Dynamic finite-size scaling at first-order transitions

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Phase Transitions

Background:

• Finite-size systems near a first-order transition (FOT) exhibit complex dynamics.
• The coexistence region, where distinct phases coexist, is characterized by long timescales due to phase tunneling.

Purpose of the Study:

• To develop a general dynamic finite-size scaling (DFSS) theory for systems near FOTs.
• To provide exact predictions for dynamical scaling functions in the coexistence region.
• To validate the DFSS theory using established physical models.

Main Methods:

• Development of a DFSS theory tailored for the coexistence region of FOTs.
• Modeling the dynamics as a two-state coarse-grained system for timescales near phase tunneling.
• Numerical simulations of the 2D Ising model (driven by magnetic field) and the 20-state Potts model (thermal FOT) using relaxational dynamics.

Main Results:

• The DFSS theory accurately describes the dynamic behavior in the coexistence region.
• Exact predictions for dynamical scaling functions were derived.
• Numerical results from both Ising and Potts models provided strong confirmation of the DFSS theory.

Conclusions:

• The developed DFSS theory is a robust framework for understanding dynamics at FOTs.
• The two-state coarse-grained dynamics effectively captures the essential physics of phase tunneling.
• The theory's validity is confirmed across different types of FOTs and models.