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The Polchinski version of the exact renormalisation group equations isapplied to multicritical fixed points, which are present for dimensions betweentwo and four, for scalar theories using both the local potential approximationand its extension, the derivative expansion. The results are compared with theepsilon expansion by showing that the non linear differential equations may belinearised at each multicritical point and the epsilon expansion treated as aperturbative expansion. The results for critical exponents are compared withcorresponding epsilon expansion results from standard perturbation theory. Theresults provide a test for the validity of the local potential approximationand also the derivative expansion. An alternative truncation of the exact RGequation leads to equations which are similar to those found in the derivativeexpansion but which gives correct results for critical exponents to order$\epsilon$ and also for the field anomalous dimension to order $\epsilon^2$. Anexact marginal operator for the full RG equations is also constructed.

Epsilon Expansion for Multicritical Fixed Points and Exact Renormalisation Group Equations