2023/10/13 by Greco, Damiano, Guopeng Li, Li, Guopeng +5
Engineering · #35Q55 #60H30 #60H40 #81T08 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Hydrocarbon exploration and reservoir analysis #Mathematical Physics (math-ph) #Phase Equilibria and Thermodynamics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2310.08783
openalex publication_date 2023/10/13 · openalex created_date 2023/10/17 · openalex updated_date 2026/07/28
We study Gibbs measures on the d-dimensional torus with L2-(super)critical focusing interaction potentials. We establish a precise divergence rate of the partition function as we remove regularization, where the optimal constant is given by (i) (the negative of) the minimum value of the Hamiltonian given an L2-constraint in the L2-critical case and (ii) the optimal constant for certain Bernstein's inequality in the mass-supercritical case. In particular, our result in the L2-critical case precisely quantifies the phase transition of the focusing Gibbs measure at the critical L2 threshold, previously studied by Lebowitz, Rose, and Speer (1988) and Sosoe, Tolomeo, and the fourth author (2022).