Parabolic stochastic quantisation of the fractional ${\Phi }_3^4$ model in the full subcritical regime

Abstract

We present a construction of the measure of the fractional ${\Phi }^4$ Euclidean quantum field theory on ${\mathbb{R}}^3$ in the full subcritical regime via parabolic stochastic quantisation. Our approach is based on a truncated flow equation for the effective description of the model at sufficiently small scales and on coercive estimates for the nonlinear stochastic partial differential equation describing the interacting field. The constructed measure is translation invariant, reflection positive, and has quartic exponential tails.