2-DIMENSIONAL ISING-MODEL IN AN ANNEALED RANDOM-FIELD

The critical behavior of the two-dimensional Ising model (square latti ce, exchange constant J) in an uniform field, and in an annealed rando m field is considered. The random field is generated by decorating the horizontal and vertical bonds of the lattice, and it satisfies an arb itrary distribution which is imposed by introducing a pseudo-chemical potential. By decimating the decorating variables the model can be map ped onto a homogeneous Ising model with effective exchange constant J' and effective external field h', dependent on the temperature. These parameters, which satisfy a set of coupled equations, depend on the sp in average and nearest-neighbor two-spin correlation, and are obtained numerically. For the symmetric field distribution p(h(i)) = 1/2[delta (h + h(i)) + delta(h - h(i))] the mapping of the critical frontier on the (K' = beta J', H' = beta h') plane onto the (K = beta J, H = beta h) plane is determined and, as in the model introduced by Essam and Pl ace, there is a region on the (K, H) plane which cannot be reached fro m any real values of (K', H'). The critical exponents are determined n umerically, and it is shown that they do not satisfy renormalization r elations obtained for their model.