Kawasaki dynamics with infinite-range spin exchange

J. M. Nunes da Silva, Eduardo Lage

G. De Smedt, C. Godr�che, J. M. Luck

Zhu Jian-Yang, Zhu Han

We generalize Kawasaki's dynamics, spin-pair exchange mechanism, to a spin-pair redistribution mechanism, and we present a normalized redistribution probability. As an application, we treat the one-dimensional kinetic Gaussian model and obtain the exact diffusion equation and the temperature-dependent diffusion coefficient. We find that the diffusion process can slow down infinitely near the critical point and obtain the critical dynamic exponent z = 2 that is independent of the assumed mechanism, either Glauber-type or Kawasaki-type.

José F. F. Mendes, Eduardo Lage

Monte Carlo simulations and finite-size scaling were used to study the one-dimensional BEG (Blume-Emergy-Griffiths) model under the influence of two competing dynamics: single spin flip (Glauber dynamics at finite temperature T) and random exchange to two spins (Kawasaki dynamics at infinite temperature). The phase diagram shows first- and second-order phase transitions. The critical exponents are obtained for different values of the rates and the range of the exchanges. The authors find beta =0.325+or-0.020, gamma =0.996+or-0.004 and nu =1.71+or-0.01 for long-range exchanges and equal intrinsic rates. However, for different rates and the nearest-neighbour exchanges they obtain beta =0.07+or-0.03, gamma =1.60+or-0.06 and nu =1.53+or-0.08, thus exhibiting non-universal behaviour.

Joachim Stolze, Oleg Derzhko, Taras Krokhmalskii

Simone Artz, Steffen Trimper

Using a quantum formulation of the master equation we study a kinetic Ising model with competing stochastic processes: the Glauber dynamics with probability p and the Kawasaki dynamics with probability 1-p. Introducing explicitly the coupling to a heat bath and the mutual static interaction of the spins the model can be traced back exactly to a Ginzburg–Landau functional when the interaction is of long range order. The dependence of the correlation length on the temperature and on the probability p is calculated. In case that the spins are subject to flip processes the correlation length disappears for each finite temperature. In the exchange dominated case the system is strongly correlated for each temperature.