Spectral properties of weakly coupled Landau-Ginzburg stochastic models

We study the existence of bound states in the generator of the stochastic dynamics associated to weakly coupled lattice Landau-Ginzburg models. By analyzing the Bethe-Salpeter kernel in the ladder approximation, these states are shown to exist if the polynomial interaction has a negative quartic term and the lattice dimension is smaller than 3. Asymptotic values for the masses are also obtained, giving precise relaxation rates for even correlations.