We present the Monte Carlo study of spin systems with randomness.
The order of phase transition of the three-dimensional three-state Potts model in random fields is analyzed using the Monte Carlo method. In accordance with the prediction of the theory, we found the phase transition becomes continuous when the external field is strong enough.
We studied the domain kinetics of the two-dimensional ferromagnetic Ising model with random coupling constants which have a Gaussian distribution with the mean value J and the width ΔJ. Here ΔJ is smaller than J. When this system is quenched to low temperature, the evolution of initially circular domains are observed. We find that the relation between the decay time t and the size R of the domain is given as
$R(t)=C\; t^a \qquad \qquad (1)$
where a is an exponent less than 1/2 varying with ΔJ and the quenching temperature T, whereas a is 1/2 for pure system. The larger ΔJ and the lower the temperature T is, the smaller the exponent becomes.
Next, the domain kinetics of the random field Ising model was studied. The logarithmic growth predicted by the theories was not observed. The power law of (1) also describes the growth behavior of the random field Ising model. The exponent a decreases as the random field strength increases. We considered a generalization of the random field Ising model which has random coupling constants. We found that the randomness of coupling contants makes the domain kinetics much slower than the usual random field Ising model.
