New results concerning the statistics of, in particular,p random walkers on a line whose paths do not cross are reported, extended, and interpreted. A general mechanism yielding phase transitions in… Expand

Derivations of the partition function of the Ising model on a general planar lattice L, which proceed via an associated dimer problem and use Pfaffians, are simplified by constructing a lattice LΔ… Expand

Abstract An important, even though physically oversimplified model of a system (e.g. solution or gas) containing diatomic molecules is that of a lattice occupied by ‘rigid dimers’ (e.g. Fowler and… Expand

The theory of critical phenomena in systems at equilibrium is reviewed at an introductory level with special emphasis on the values of the critical point exponents α, β, γ,..., and their… Expand

Long-range components of the interaction in statistical mechanical systems may affect the critical behavior, raising the system's 'effective dimension'. Presented here are explicit implications to… Expand