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The European Physical Journal B

Non-equilibrium phase transitions in the two-temperature Ising model with Kawasaki dynamics

B. Renklioglu, M. Cemal Yalabık

Published Dec 1, 2012• 4 citations
Publisher
DOI
10.1140/epjb/e2012-30726-5

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The critical temperature of the paramagnetic-ferromagnetic phase transition on the Ising model of the square lattice is studied by means of the Monte Carlo method.The Glauber and Kawasaki dynamics are considered in the calculation for the stochastic and sequent processes and their effects on the critical temperatures are discussed.It's shown that the critical temperature can be calculated in the stochastic and sequent processes when the Glauber dynamic is in the lead.But only in the stochastic process the critical temperature can be calculated when the Kawasaki dynamic is in the lead.
We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temperature T. The dynamics of the system is simulated by two competing stochastic processes: the two-spin-exchange Kawasaki kinetics at temperature T>0 and the one-spin-flip Glauber dynamics at T(G)-->0(-), which mimics the increase of the energy of the system. These two processes have probabilities 1-p and p, respectively. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. Contrary to the ferromagnetic case, the phase diagram obtained does not exhibit the phenomenon of self-organization: for any nonzero value of the competing parameter p, and for any value of T, the only stationary phase which remains is the ferromagnetic one. At the phase transition between the antiferromagnetic and paramagnetic phases, at p=0, the values found for the critical exponents agree with those of the corresponding equilibrium Ising model.
We investigate the temporal evolution of a ferromagnetic system of Ising spins evolving under Kawasaki dynamics from a random initial condition, in spatial dimensions one and two. We examine in detail the asymptotic behaviour of the two-time correlation and response functions. The linear response is measured without applying a field, using a recently proposed algorithm. For the chain at vanishingly small temperature, we introduce an accelerated dynamics which has the virtue of projecting the system into the asymptotic scaling regime. This allows us to revisit critically previous works on the behaviour at large time of the two-time autocorrelation and response functions. We also analyse the case of the two-dimensional system at criticality. A comparison with Glauber dynamics is performed in both dimensionalities, in order to underline the similarities and differences in the phenomenology of the two dynamics.