Critical relaxational dynamics at the continuous transitions of three-dimensional spin models with Z2 gauge symmetry

We characterize the dynamic universality classes of a relaxational dynamics under equilibrium conditions at the continuous transitions of three-dimensional (3D) spin systems with Z2 gauge symmetry. In particular, we consider the pure lattice Z2 gauge model and the lattice Z2 gauge XY model, which present various types of transitions: topological transitions without a local order parameter and transitions characterized by both gauge-invariant and non-gauge-invariant XY order parameters. We consider a standard relaxational (locally reversible) Metropolis dynamics and determine the dynamic critical exponent z that characterizes the critical slowing down of the dynamics as the continuous transition is approached. At the topological Z2 gauge transitions we find z=2.55(6). Therefore, the dynamics is significantly slower than in Ising systems - z≈2.02 for the 3D Ising universality class - although 3D Z2 gauge systems and Ising systems have the same static critical behavior because of duality. As for the nontopological transitions in the 3D Z2 gauge XY model, we find that their critical dynamics belong to the same dynamic universality class as the relaxational dynamics in ungauged XY systems independently of the gauge-invariant or non-gauge-invariant nature of the order parameter at the transition.