MODIFIED SCALING RELATION FOR THE RANDOM-FIELD ISING-MODEL

We investigate the low-temperature critical behavior of the three-dime nsional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature T --> 0 the usual scaling relations h ave to be modified as far as the exponent alpha of the specific heat i s concerned. At zero temperature, the Rushbrooke equation is modified to alpha + 2 beta + gamma = 1, an equation which we expect to be valid also for other systems with similar critical behavior. We test the sc aling theory numerically for the three-dimensional random-field Ising system with Gaussian probability distribution of the random fields by a combination of calculations of exact pound states with an integer op timization algorithm and Monte Carlo methods. By a finite-size scaling analysis we calculate the critical exponents nu approximate to 1.0, b eta approximate to 0.05, <(gamma)over bar> = 2.9, gamma approximate to 1.5 and alpha approximate to -0.55. (C) 1998 Elsevier Science B.V. Al l rights reserved.