Criticality of compact and noncompact quantum dissipative $Z_4$ models in $(1+1)$ dimensions

Abstract

Using large-scale Monte Carlo computations, we study two versions of a $(1+1)D$ $Z_4$-symmetric model with Ohmic bond dissipation. In one of these versions, the variables are restricted to the interval $[0,2\pi >$, while the domain is unrestricted in the other version. The compact model features a completely ordered phase with a broken $Z_4$ symmetry and a disordered phase, separated by a critical line. The noncompact model features three phases. In addition to the two phases exhibited by the compact model, there is also an intermediate phase with isotropic quasi-long-range order. We calculate the dynamical critical exponent $z$ along the critical lines of both models to see if the compactness of the variable is relevant to the critical scaling between space and imaginary time. There appears to be no difference between the two models in that respect, and we find $z\approx 1$ for the single phase transition in the compact model as well as for both transitions in the noncompact model.

References in corpus (10)

• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
• Theory of the Quantum Critical Fluctuations in Cuprates
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• A cluster algorithm for resistively shunted Josephson junctions
• Thermodynamic Properties near the onset of Loop-Current Order in high-$T_c$ superconducting cuprates
• True and quasi long-range order in the generalized $q$-state clock model
• Comment on `Six-state clock model on the square lattice: Fisher zero approach with Wang-Landau sampling'
• Floating phase in a dissipative Josephson junction array
• Monte Carlo simulations of dissipative quantum Ising models
• Effective theory of fluctuating circulating currents in high-Tc cuprates

Cited by in corpus (3)

• Three distinct types of quantum phase transitions in a (2+1)-dimensional array of dissipative Josephson junctions
• Quantum criticality in a dissipative (2+1)-dimensional XY model of circulating currents in high-Tc cuprates
• Phases and Phase Transitions of the Disordered Quantum Clock Model