Classical and quantum KMS states on spin lattice systems

In this talk, we present new sufficient conditions for subcriticality in classical and quantum spin lattice systems, expressed through the uniqueness of Kubo-Martin-Schwinger (KMS) states. Our approach relies on a non-commutative analogue of the Kirkwood-Salzburg equations combined with a novel decomposition of local observables. These techniques significantly broaden the range of interactions to which the criteria apply and yield improved lower bounds on the subcritical inverse temperature. The framework is robust enough to handle models without any assumptions on the single-site potentials. This is joint work with L. Pettinari and C. J. F. van de Ven.