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Shape of crossover between mean-field and asymptotic critical behavior in a three-dimensional Ising lattice

Mikhail A. Anisimov, Erik Luijten, V. A. Agayan +2 more

arXiv:cond-mat/9810252Physics Letters ADec 1, 199922 citations

Non-equilibrium phase transitions in one-dimensional kinetic Ising models

Nóra Menyhárd, Géza Ódor

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. 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 tricritical point is located at the Glauber ( delta =0) limit. Corrections to the 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 beta of the order parameter which is obtained as beta approximately=1.0.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. 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 tricritical point is located at the Glauber ( delta =0) limit. Corrections to the 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 beta of the order parameter which is obtained as beta approximately=1.0.

arXiv:cond-mat/9504061Journal of Physics A Mathematical and GeneralAug 21, 199550 citations

One-dimensional kinetic Ising model with competing spin-flip and spin-exchange dynamics: Ordering in the case of long-range exchanges

Michel Droz, Zoltàn Ràcz, P. Tartaglia

Ordering of a one-dimensional stochastic Ising model evolving by a combination of spin flips and spin exchanges is investigated. The spin-flip rates satisfy detailed balance for the equilibrium state of the Ising model at temperature T, while the spin exchanges are random and of arbitrary range. Analytical methods and Monte Carlo simulations are used to show that, depending on the details of the spin-flip rate, finite-temperature phase transition may or may not occur in the system. When ordering occurs, it is of mean-field type and the scaling function describing the finite-size scaling of the magnetization fluctuations is found to be indistinguishable from that of an equilibrium Ising model with infinite-range interaction.Ordering of a one-dimensional stochastic Ising model evolving by a combination of spin flips and spin exchanges is investigated. The spin-flip rates satisfy detailed balance for the equilibrium state of the Ising model at temperature T, while the spin exchanges are random and of arbitrary range. Analytical methods and Monte Carlo simulations are used to show that, depending on the details of the spin-flip rate, finite-temperature phase transition may or may not occur in the system. When ordering occurs, it is of mean-field type and the scaling function describing the finite-size scaling of the magnetization fluctuations is found to be indistinguishable from that of an equilibrium Ising model with infinite-range interaction.

Physical Review AJun 1, 199035 citations

Crossover Critical Behavior in the Three-Dimensional Ising Model

Young C. Kim, Mikhail A. Anisimov, Jan V. Sengers +1 more

arXiv:cond-mat/0203190Journal of Statistical PhysicsMar 1, 200349 citations

Critical dynamics of finite Ising model

Jean Christian Anglès d’Auriac, R. Maynard, R. Rammal

Journal of Statistical PhysicsJun 1, 198227 citations

Phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk of kinks

Nóra Menyhárd, Géza Ódor

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 characterizing 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. The 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.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 characterizing 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. The 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.

arXiv:cond-mat/9607089Journal of Physics A Mathematical and GeneralDec 7, 199652 citations

Crossover from Ising to mean-field critical behavior in a kinetic Ising model with competing flip and exchange dynamics

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