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arXiv · 2511.12651

Subcriticality at High Temperatures in Spin Lattice Systems

Nicolò Drago·Lorenzo Pettinari·Christiaan J. F. van de Ven
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Abstract

We provide new sufficient conditions for subcriticality of classical and quantum spin lattice systems, formulated in terms of the uniqueness of Kubo-Martin-Schwinger (KMS) states. This is achieved by exploiting a non-commutative analog of the Kirkwood-Salzburg equations together with a novel decomposition of local observables. In contrast to standard approaches \cite{Bratteli_Robinson_97,Frohlich_Ueltschi_2015}, our condition is uniform with respect to the dimension of the single-site Hilbert space. Moreover, unlike the results of \cite{Drago_Pettinari_Van_de_Ven_2025}, which required control over the growth of the derivatives of the interaction potentials, our result only involves estimating the natural $C^*$-norm of these potentials. This substantially enlarges the class of interactions for which the theorems apply and provides better lower bounds on the subcritical inverse temperature.

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Nicolò Drago, Lorenzo Pettinari, Christiaan J. F. van de Ven. 2025-11-16. Subcriticality at High Temperatures in Spin Lattice Systems. https://arxiv.org/abs/2511.12651

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