Gibbs states on space-time (Q1841539)

The authors construct the Gibbs states on the space of trajectories \(\Omega= {\mathcal C}({\mathbf R}, {\mathbf R})^{Z^d}\). This construction is done by two different methods. The first method uses the idea that Gibbs states on \(\Omega\) are solutions of infinite-dimensional stochastic differential equations. The second construction is based on the method of cluster expansions. The authors show the existence and regularity of the limiting Gibbs states for a class of Hamiltonians indexed by small parameter.