Thermally driven phase transitions near the percolation threshold in two dimensions

It is shown that thermally driven magnetic critical phenomena just above and just below the percolation limit can be usefully analysed using scaling theory, a further assumption concerning cluster connectivity provides quantitative predictions for critical exponents and scaling functions that should be experimentally testable. In particular, reasonable agreement is found with recent experimental results of Birgeneau, Cowley, Shirane and Guggenheim (Phys. Rev. Lett., vol.37, p.940 (1976)) on the quasi-two-dimensional random magnet Rb₂Mn_pMg_1-pF₄.