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 ${\xi }_p$ at the percolation threshold. It is argued that thermodynamic functions should be scaling functions of $\frac{{\xi }_1\mathrm{}\left(T\right)\mathrm{}}{l}$, where ${\xi }_1\mathrm{}\left(T\right)\mathrm{}$ is the correlation length of a one-dimensional spin system. The implications of this scaling ansatz are discussed.