Mean-field theory of statistical assemblies of sterically interacting lines

Abstract

Statistical assemblies of lines on simple cubic lattices are considered. Beginning with a gas of diffusion loops we add steric interaction and chains. The interaction is treated by a mean-field ansatz strictly valid only for d > 4. Phase transitions are characterized by the appearance of infinite lines. The formalism can be applied to thermally equilibrated polymers, defect models of phase transitions, and to the high-temperature expansions of the n -vector model. The classical theories of phase transitions including the Gaussian approximations are recovered, in particular their critical exponents