Work

Parabolic stochastic quantisation of the fractional $\Phi^{4}_{3}$ model in the full subcritical regime

Year: 2026

Type: article

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.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1816

Authors: Paweł Duch, Massimiliano Gubinelli, Paolo Rinaldi

Institutions: École Polytechnique Fédérale de Lausanne, Adam Mickiewicz University in Poznań, University of Oxford, University of Pavia

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutsche Forschungsgemeinschaft, Narodowym Centrum Nauki

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G2740759098, G8847963564