Critical relaxational dynamics at the continuous transitions of three-dimensional spin models with ${\mathbb{Z}}_2$ gauge symmetry

Abstract

We characterize the dynamic universality classes of a relaxational dynamics under equilibrium conditions at the continuous transitions of three-dimensional (3D) spin systems with a ${\mathbb{Z}}_2$-gauge symmetry. In particular, we consider the pure lattice ${\mathbb{Z}}_2$-gauge model and the lattice ${\mathbb{Z}}_2$-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 ${\mathbb{Z}}_2$-gauge transitions we find $z=2.55(6)$. Therefore, the dynamics is significantly slower than in Ising systems -- $z\approx 2.02$ for the 3D Ising universality class -- although 3D ${\mathbb{Z}}_2$-gauge systems and Ising systems have the same static critical behavior because of duality. As for the nontopological transitions in the 3D ${\mathbb{Z}}_2$-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 nongauge-invariant nature of the order parameter at the transition.

12 pages, 5 pdf figures

References in corpus (14)

• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The critical exponents of the superfluid transition in He4
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Monte Carlo study of an improved clock model in three dimensions
• Gauge theory picture of an ordering transition in a dimer model
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
• Higher-charge three-dimensional compact lattice Abelian-Higgs models
• Numerical study of duality and universality in a frozen superconductor
• Multicritical point of the three-dimensional Z_2 gauge Higgs model
• Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
• Classification of nematic order in 2+1D: Dislocation melting and $O(2)/Z_N$ lattice gauge theory
• Relaxational dynamics in 3D randomly diluted Ising models
• Criticality of O(N) symmetric models in the presence of discrete gauge symmetries
• Three-dimensional lattice SU($N_c$) gauge theories with multiflavor scalar fields in the adjoint representation

Cited by in corpus (4)

• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Universal exotic dynamics in critical mesoscopic systems: Simulating the square root of Avogadro's number of spins
• Finite-temperature topological transitions in the presence of quenched uncorrelated disorder
• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models