Statistical mechanical methods in particle structure analysis of lattice field theories. Pt. 1

We analyze the particle structure of lattice field theories, in particular of lattice gauge theories with matter fields. We introduce and exploit the idea that particle structure in lattice field theory is intimately related to the statistical mechanics of fluctuating random paths and random tubes which arise in random walk and random surface representations of the lattice theories. Our methods permit us to understand, among other things, the high-temperature behaviour of energy-energy correlations in the Ising model in four more dimensions, the glue-ball spectrum and the meson spectrum in strongly coupled lattice gauge theory, and the special features of quantum mechanical binding in one and two dimensions. (orig.)