We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the nonequilibrium phase transition. Obtained critical exponents indicate that the two-dimensional kagome-lattice kinetic Ising model belongs to the same universality class with the corresponding Ising model in equilibrium. Moreover, dynamic critical exponent of the local moves used in simulations is determined with high precision. Our numerical results are compatible with the previous ones on kinetic Ising models.
We study the phase diagram and critical behaviors of three-dimensional lattice
Z2-gauge
N-vector models, in which an
N-component real field is minimally coupled with
Z2-gauge link variables. These models are invariant under global
O(N) and local
Z2 transformations. They present three phases characterized by the spontaneous breaking of the global
O(N) symmetry and by the different topological properties of the
Z2-gauge correlations. We address the nature of the three transition lines separating the three phases. The theoretical predictions are supported by numerical finite-size scaling analyses of Monte Carlo data for the
N=2 model. In this case, continuous transitions can be observed along both transition lines where the
N-component spins order, in the regimes of small and large inverse gauge coupling
K. Even though these continuous transitions belong to the same
XY universality class, their critical modes turn out to be different. When the gauge variables are disordered (small
K), the relevant order-parameter field is a gauge-invariant bilinear combination of the vector field. On the other hand, when the gauge variables are ordered (large
K), the order-parameter field is the gauge-dependent
N-vector field, whose critical behavior can only be probed by using a stochastic gauge fixing that reduces the gauge freedom.
We investigate the critical properties of the three-dimensional antiferromagnetic RP^{N-1} model, which is characterized by a global O(N) symmetry and a discrete Z_{2} gauge symmetry. We perform a field-theoretical analysis using the Landau-Ginzburg-Wilson (LGW) approach and a numerical Monte Carlo study. The LGW field-theoretical results are obtained by high-order perturbative analyses of the renormalization-group flow of the most general Φ^{4} theory with the same global symmetry as the model, assuming a gauge-invariant order-parameter field. For N=4 no stable fixed point is found, implying that any transition must necessarily be of first order. This is contradicted by the numerical results that provide strong evidence for a continuous transition. This suggests that gauge modes are not always irrelevant, as assumed by the LGW approach, but they may play an important role to determine the actual critical dynamics at the phase transition of O(N) symmetric models with a discrete Z_{2} gauge symmetry.
We investigate the critical phenomena of the three-dimensional (3D)
SU(2) gauge glass model, which can be regarded as the
O(4) spin-glass model with gauge symmetry. Using Monte Carlo simulations and the non-equilibrium relaxation method, we examine the critical behavior along phase boundaries across various degrees of disorder. Consistent with previous studies, we verify that weak disorder is irrelevant to the universality class; the critical behavior of the ferromagnetic-paramagnetic transition remains in the 3D
O(4) universality class of the pure ferromagnetic system. Additionally, we demonstrate that the paramagnetic-spin glass transition exhibits universal critical behavior independent of the disorder. Our findings provide valuable insights into the fundamental properties and universality of gauge glass models.
We employed Monte Carlo simulations and short-time dynamic scaling to determine the static and dynamic critical exponents for the generalized two-dimensional Blume-Capel model of spin-3/2. We showed that the critical behavior at the second-order phase-transition line between the paramagnetic and ferromagnetic phases is in the same universality class of the two-dimensional Ising model. However, at the double critical end point, which is present in the phase diagram of the model, the critical exponent beta , associated to the order parameter, is different from that of the Ising model.
The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (pinned) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth-order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes (L). From the finite size analysis of dynamic order parameter and the dynamic susceptibility , we have estimated the critical exponents and (measured from the data read at the critical temperature obtained from Binder cumulant), and (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where and ), within the limits of statistical errors.