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We study the dynamics of the spin-1/2 random transverse Ising model in the high-temperature limit by means of the method of recurrence relations. We analyze two types of disorder: a disorder on the transverse field, and a disorder on the exchange coupling. We find that the dynamics undergoes a crossover from a central peak behavior onto a collective mode behavior as a function of the disorder. ͓S0163-1829͑99͒04937-1͔ PHYSICAL REVIEW B 1 OCTOBER 1999-I VOLUME 60, NUMBER 13 PRB 60 0163-1829/99/60͑13͒/9555͑6͒/$15.00 9555

Using the Finite Size Scaling Renormalisation Group we obtain the two-dimensional flow diagram of the Blume-Capel model, for S = 1 and S = 3/2. In the first case our results are similar to those of Mean Field Theory, which predicts the existence of first and second order transitions whith a tricritical point.In the second case, however, our results are different. While we obtain, in the S = 1 case, a phase diagram presenting a multicritical point, the Mean Field approach predicts only a second order transition and a critical end point.Work partially supported by Brazilian agencies FINEP, CNPq, CAPES and FAPEMIG.