Scaling theory of phase transitions in diluted systems near the percolation threshold

A heuristic picture, due to de Gennes and to Skal and Shklovskii, of a diluted lattice is used to introduce a one-dimensional path length l which diverges more rapidly than the percolation correlation length ξₚ at the percolation threshold. It is argued that thermodynamic functions should be scaling functions of ξ₁(T)l, where ξ₁(T) is the correlation length of a one-dimensional spin system. The implications of this scaling ansatz are discussed.