Collapse of the Gibbs measure for the dynamical Φ³₂-models on the infinite volume

We study the Φ³₂-measure in the infinite volume limit. This is the invariant measure for several stochastic partial differential equations including the parabolic and hyperbolic Φ³₂-models. In the large torus limit, we observe a concentration phenomenon of the Φ³₂-measure around zero, which is the single minimizer of the corresponding Hamiltonian for any fixed torus size. From our sharp estimates for the partition function, we obtain a triviality result for the Φ³₂-measure on infinite volume: the ensemble collapses onto a delta function on the zero field.