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THE SPIN-S BLUME-CAPEL RG FLOW DIAGRAM

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, as 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.