Classical and Quantum KMS States on Spin Lattice Systems

Abstract: In this talk, we discuss the classical and quantum KMS conditions in the context of spin lattice systems. Using the Berezin quantization of a 2-sphere-valued spin system on a discrete lattice, we lift a classical dynamics on the algebra of classical observables to a corresponding quantum dynamics on the algebra of quantum observables. This framework allows us to compare the notions of classical and quantum thermal equilibrium by proving that every weak* limit point of a family of quantum KMS states satisfies the classical KMS condition. Consequently, the semiclassical limit of quantum thermal equilibrium states describes classical thermal equilibrium, thereby providing further justification for the physical interpretation of the classical KMS condition. In the second part of the talk, we present new sufficient conditions for the uniqueness of both classical and quantum KMS states in the high-temperature (subcritical) regime. These conditions substantially enlarge the class of admissible interactions while also improving the lower bounds on the critical inverse temperature. In particular, they identify a common subcritical regime in which both the classical and the quantum KMS state are unique. This is joint work with L. Pettinari and C. J. F. van de Ven. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page