Nonequilibrium kinetic Ising models: phase transitions and universality classes in one dimension (original) (raw)
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Journal of Physics A: Mathematical and General, 1996
One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are now further investigated, numerically, from the point of view of the underlying spin system. Critical exponents characterising its statics and dynamics are reported. It is found that the influence of the PC transition on the critical exponents of the spins is strong and the origin of drastic changes as compared to the Glauber-Ising case can be traced back to the hyperscaling law stemming from directed percolation. Effect of an external magnetic field, leading to directed percolation type behaviour on the level of kinks, is also studied, mainly via the generalized mean field approximation.
Non-equilibrium phase transitions in one-dimensional kinetic Ising models
Journal of Physics A: Mathematical and General, 1995
A family of nonequilibrium kinetic Ising models, introduced earlier, evolving under the competing effect of spin flips at zero temperature and nearest neighbour random spin exchanges is further investigated here. By increasing the range of spin exchanges and/or their strength the nature of the phase transition 'Ising-to-active' becomes of (dynamic) mean-field type and a first order tricitical point is located at the Glauber (δ = 0) limit. Corrections to mean-field theory are evaluated up to sixth order in a cluster approximation and found to give good results concerning the phase boundary and the critical exponent β of the order parameter which is obtained as β ≃ 1.0.
One-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk
Journal of Physics A: Mathematical and General, 1994
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges at T = ∞ are investigated numerically from the point of view of a phase transition. Branching annihilating random walk of the ferromagnetic domain boundaries determines the steady state of the system for a range of parameters of the model. Critical exponents obtained by simulation are found to agree, within error, with those in Grassberger's cellular automata.
Physica A: Statistical Mechanics and its Applications, 1991
A two-dimensional kinetic Ising model evolving by a combination of spin flips at temperature T and spin exchanges which are random and of arbitrary range is investigated. We present a meanfield theory and compare its predictions with Monte Carlo simulations. The results indicate that the equilibrium Ising transition that is present without the spin exchanges turns into a mean-field transition as soon as the spin-exchange rate is different from zero. The crossover from Ising to mean-field critical behavior is characterized by an exponent, ~ ~ 2, equal to the analogous crossover exponent in equilibrium systems.
Kinetic phase transition in the mixed-spin Ising model
Brazilian Journal of Physics, 2004
In this work we studied a ferromagnetic mixed-spin Ising model including a single ion crystal-field term. The model system consists of two interpenetrating sublattices with spins σ = 1/2 and S = 1. The spins σ = 1/2 occupy the sites of one sublattice, their nearest-neighbours are spins S on the other sublattice, and vice versa. The system is in contact with a heat bath, the spins flipping according to the Metropolis transition rate and, at the same time, subject to an external flow of energy, which is simulated by a two-spin flip process. The model is studied via the dynamical pair approximation and through Monte Carlo simulations. We have determined the phase diagram of the model in the plane crystal-field D versus competition parameter p. The parameter p accounts for the competition between the one-and two-spin flip processes. In the pair approximation, the phase diagram, at high temperatures, present three phases separated by two transition lines: a continuous transition line between the ferromagnetic and paramagnetic phases, and a first-order transition line between the paramagnetic and antiferromagnetic phases. However, Monte Carlo simulations predict the same topology for the phase diagram as the pair approximation, but all the transition lines are continuous for any value of the temperature.
Nonequilibrium phase transition in an Ising model without detailed balance
Physical review. E, 2020
We study a two-dimensional ferromagnetic Ising model in which spins are updated using modified versions of the Metropolis and Glauber algorithms. These update rules do not obey the detailed balance condition. The steady-state behavior of the model is studied using molecular field theory and Monte Carlo simulations. This model is found to exhibit a nonequilibrium phase transition from a "paramagnetic" state with zero magnetization to a "ferromagnetic" state with nonzero magnetization as the variable that plays the role of temperature in the spin updates is decreased. From detailed Monte Carlo simulations using the modified Metropolis algorithm, we demonstrate explicitly the nonequilibrium nature of the transition and show that it cannot be described as an equilibrium transition with an effective temperature different from the temperature used in the spin updates. The critical exponents that characterize the singular behavior near this continuous phase transition a...
2020
In this paper, we theoretically study the critical properties of the classical spin-1 Ising model using two approaches: 1) the analytical low-temperature series expansion and 2) the numerical Metropolis Monte Carlo technique. Within this analysis, we discuss the critical behavior of one-, two- and three-dimensional systems modeled by the first-neighbor spin-1 Ising model for different types of exchange interactions. The comparison of the results obtained according the Metropolis Monte Carlo simulations allows us to highlight the limits of the widely used mean-field theory approach. We also show, via a simple transformation, that for the special case where the bilinear and bicubic terms are set equal to zero in the Hamiltonian the partition function of the spin-1 Ising model can be reduced to that of the spin-1/2 Ising model with temperature dependent external field and temperature independent exchange interaction times an exponential factor depending on the other terms of the Hamilt...
Journal of Physics A: Mathematical and General, 1997
One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are investigated here numerically from the point of view of the underlying spin system. The dynamical persistency exponent Θ and the exponent λ characterising the two-time autocorrelation function of the total magnetization under nonequilibrium conditions are reported. It is found that the PC transition has strong effect: the process becomes non-Markovian and the above exponents exhibit drastic changes as compared to the Glauber-Ising case.