2025/06/26 by Nikolay A. Barashkov, Barashkov, Nikolay, Trishen S. Gunaratnam +1
Mathematics · #60H30 #81T08 #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2506.21466
openalex publication_date 2025/06/26 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
We prove that the φ43 model satisfies a version of Segal's axioms in the special case of three-dimensional tori and cylinders. As a consequence, we give the first proof that this model satisfies a Markov property and we characterize its boundary law up to absolutely continuous perturbations. In addition, we use Segal's axioms to give an alternative construction of the φ43 Hamiltonian on two-dimensional tori as compared with Glimm (Comm. Math. Phys., 1968). We exploit this probabilistic approach to prove novel fundamental spectral properties of the Hamiltonian, such as discrete spectrum and a Perron-Froebenius type result on its ground state. The key technical contributions of this article are the development of tools to analyze φ43 models with rough boundary conditions. We heavily use the variational approach to φ43 models introduced in Barashkov and Gubinelli (Duke, 2020) that is based on the Boué-Dupuis formula and dual to Polchinski's continuous renormalization group.