Equilibrium dynamics of continuous unbounded spin systems

Abstract

The relaxation properties of the Glauber and Kawasaki dynamics are studied for large lattice systems of unbounded continuous spins. For this purpose the logarithmic Sobolev inequality is deduced for the canonical ensemble in two cases. In the first case, the Hamiltonian consists of a sum of superquadratic single-site potentials. In the second case, the Hamiltonian also has a weak two-body interaction. For technical reasons, the single-site potential is a perturbation of a quadratic potential in this case. The scaling of the logarithmic Sobolev constant is optimal in the system size and independent of the boundary data of the system.