We consider the q-state Potts model with correlated random interactions such that their correlations decay at large distances as ∼$R^{\mathrm{-}\left(d\mathrm{-}a\right)}$. Applying the renormalization group and a double (ε,${\epsilon }_a$) expansion, we derive the scaling form of the equation of state to linear order in ε=6-d and ${\epsilon }_a$=a-2. In the limit q→1, which describes correlated percolation, the critical amplitudes $A^{\pm }$ associated with the mean number of clusters F∼$A^{\pm }$‖t${\Vert }^{2\mathrm{-}\alpha }$ are shown to diverge when α approaches a negative integer as a function of ${\epsilon }_a$.

• Received 30 January 1987

DOI:https://doi.org/10.1103/PhysRevB.36.769