THE RENORMALIZATION OF PROBABILITY-DISTRIBUTIONS IN THE RANDOM FIELD PROBLEM

The authors study the Ising ferromagnet in a random field following the renormalisation of the distribution of random fields. The disorder in the local field induces fluctuations in the exchange couplings which are taken into account. The method allows a straightforward determination of the exponents associated with the zero-temperature fixed point which governs the critical behaviour along the critical line and in particular the critical slowing down. They find the correlation length exponent v=1.0 which is in very good agreement with numerical calculations. They also obtain the crossover exponent for small random fields.