For the system in which correlations between quenched defect positions fall as mod x-x' mod -a (a=4- epsilon - epsilon d >0) the epsilon , epsilon d -expansions of the critical exponents are obtained up to the third order. It is shown that if the task of finding the critical exponents for a system with uncorrelated quenched point defects is solved at order epsilon m of the epsilon -expansion, then the critical exponents for the system considered can be simply obtained up to (m+1)th order of the epsilon , epsilon d expansion. The calculations are carried out completely in the special case of the uniaxial magnet.
The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its extension, the derivative expansion. The results are compared with the epsilon expansion by showing that the non linear differential equations may be linearised at each multicritical point and the epsilon expansion treated as a perturbative expansion. The results for critical exponents are compared with corresponding epsilon expansion results from standard perturbation theory. The results provide a test for the validity of the local potential approximation and also the derivative expansion. An alternative truncation of the exact RG equation leads to equations which are similar to those found in the derivative expansion but which gives correct results for critical exponents to order ε and also for the field anomalous dimension to order ε 2. An exact marginal operator for the full RG equations is also constructed.