Melting behaviour of percolating solids

Abstract

The authors consider the melting behaviour of randomly percolating solids and of porous solids in three dimensions. It is argued that the melting temperature T_m reaches zero (T_m(p_c)=0) at the percolation point (p_c) and varies near p_c as T_m approximately (p-p_c)^tau , where tau approximately=4.0 is the elastic exponent. Similar behaviour is also predicted for melting in two dimensions. It is further proposed that the transition (for dimension d>2) becomes continuous at p_c and the amount of discontinuity (e.g. in entropy Delta S_m) decreases monotonically to zero at p_c where, asymptotically close to p_c, a mean-field-type argument indicates that Delta S_m approximately exp(-A/(p-p_c)^tau-beta), where beta (approximately=0.4 in three dimensions) is the percolation order-parameter exponent.