Random-field critical scaling in a model of dipolar glass and relaxor ferroelectric behavior.

Heat-bath Monte Carlo simulations have been used to study a 12-state discretized Heisenberg model with a type of random field on simple cubic lattices of size 128×128×128. The 12 states correspond to the [110] directions of a cube. The model has the standard nonrandom two-spin exchange term with coupling energy J and a random field which consists of adding an energy h_{R} to two of the 12 spin states, chosen randomly and independently at each site. We report on the case h_{R}/J=3, which has a sharp phase transition at about T_{c}/J=1.40625. Below T_{c}, the model has long-range ferroelectric order oriented along one of the eight [111] directions. At T_{c}, the behavior of the peak in the structure factor, S(k), at small |k| is a straight line on a log-log plot, which gives the result η[over ¯]=1.214±0.014. The onset of orientational order below T_{c} is very rapid for this value of h_{R}. There are peaks in the specific heat and longitudinal susceptibility at T_{c}. Below T_{c} there is a strong correction to ordinary scaling, which is probably caused by the cubic anisotropy, which is a dangerous irrelevant variable.