Short-time critical dynamics in the classical cubic dimer model

TL;DR

This study investigates the short-time nonequilibrium critical dynamics of the classical cubic dimer model, revealing an unusual negative initial slip exponent and providing new insights into phase transitions beyond traditional frameworks.

Contribution

It presents the first detailed analysis of short-time critical dynamics in the 3D cubic dimer model, highlighting anomalous dynamic exponents linked to emergent symmetries and gauge constraints.

Findings

Critical temperature T_c = 0.672(1)

Static exponent ratio β/ν = 0.581(5)

Dynamic exponent z = 1.92(1) and negative initial slip exponent θ = -1.052(5)

Abstract

The classical dimer model on the cubic lattice hosts a columnar ordered phase and a disordered Coulomb phase, separated by a continuous phase transition that lies beyond the conventional Landau-Ginzburg-Wilson paradigm. While its equilibrium critical properties have been extensively studied, the nonequilibrium critical dynamics of this model--particularly in the short-time regime--remains largely unexplored. In this work, we investigate the short-time critical dynamics near the transition using large-scale Monte Carlo simulations. By quenching the system from both ordered and disordered initial states with vanishing initial correlation length, we analyze the scaling behaviors of the order parameter and its time correlation function in the short-time stage. From these scaling behaviors, we accurately determine the critical temperature $T_c = 0.672(1)$ and the static critical exponent $\beta/\nu = 0.581(5)$ according to the scaling theory of the short-time dynamics. These results are in excellent agreement with previous equilibrium studies. Moreover, we extract the dynamic critical exponent $z = 1.92(1)$ and, notably, find a negative critical initial slip exponent $\theta = -1.052(5)$. This unusual negative value contrasts sharply with the positive $\theta$ typically observed in conventional critical dynamics. We attribute this anomalous behavior to the combined effects of the emergent SO(5) symmetry at criticality and the local U(1) gauge constraint (Gauss law), which enforces a conserved diffusive dynamics and enhances fluctuations in the short-time regime. Our results provide the first comprehensive characterization of nonequilibrium short-time criticality in the three-dimensional dimer model, shedding new light on the universal dynamical features of phase transitions beyond the Landau-Ginzburg-Wilson framework.