Fermionic basis in conformal field theory and thermodynamic Bethe ansatz for excited states.
From holonomy of the Ising model form factors to -fold integrals and the theory of elliptic curves.
Functional inequalities and uniqueness of the Gibbs measure — from log-Sobolev to Poincaré
In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow Royer's approach (Royer, 1999) and obtain uniqueness by showing convergence properties of a Glauber-Langevin dynamics. The result was known when the measures on the box [-n,n]d (with free boundary conditions) satisfied the same logarithmic Sobolev inequality. We generalize this in two directions: either the constants may be...