Large deviations and free energy of Gibbs measure for the dynamical ${\mathrm{\Phi }}^3$-model in infinite volume

We study the large deviations for focusing Gibbs measures by analyzing the asymptotic behavior of the free energy in the infinite volume limit. This is the invariant Gibbs measure for the dynamical ${\mathrm{\Phi }}_2^3$-models. From our sharp estimates for the partition function, we establish a concentration phenomenon of the ${\mathrm{\Phi }}_2^3$-measure around the zero field, leading to a triviality result in the infinite volume: the ensemble collapses onto a delta function on the zero field.