Thermal melting of density waves on the square lattice

We present the theory of the effect of thermal fluctuations on commensurate p X p density wave ordering on the square lattice (p >= 3, integer). For the case in which this order is lost by a second-order transition, we argue that the adjacent state is generically an incommensurate striped state, with commensurate p-periodic long-range order along one direction, and incommensurate quasilong-range order along the orthogonal direction. We also present the routes by which the fully disordered high temperature state can be reached. For p=4, and at special commensurate densities, the 4 X 4 commensurate state can melt directly into the disordered state via a self-dual critical point with nonuniversal exponents.