Universal features in the classical statistical mechanics for a class of continuum-field nonlinear Hamiltonians

A class of one-dimensional, locally-nonlinear, dispersive Hamiltonians is defined, which includes both the sine Gordon and ø4 models. A transfer integral operator technique is used to investigate the classical statistical mechanics for this class, and several universality and scaling properties are demonstrated in the continuous field limit. Physical interpretations are suggested for these properties at both high and low temperatures in terms of fundamental nonlinear modes, including solitary-wave (soliton) excitations. Relationships are noted with alternative real-space renormalization group schemes.