Universality of the bridge functions and a semiempirical freezing criterion in two and three dimensions

A model for systems interacting via soft inverse-power potentials enables one to express the bridge function at the origin, $B\left(O\right)\mathrm{}$, directly in terms of the equation of state, and to find its physical meaning. The Lindemann, Ross, and van der Waals empirical melting criteria are unified by the empirical finding that $B\left(O\right)\mathrm{}$, calculated along the freezing line, is nearly independent of the pair potential and is nearly the same in two and three dimensions.