Subcriticality at High Temperatures in Spin Lattice Systems

Drag N, Pettinar L, Van de Ven C (2026)

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2026

Publisher: arXiv

DOI: 10.48550/arXiv.2511.12651

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 [7, 18], our condition is uniform with respect to the dimension of the single-site

Hilbert space. Moreover, unlike the results of [13], 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.

Finally, our results are flexible enough to cover situations where no assumptions are imposed

on the single-site potentials.

Authors with CRIS profile

Christiaan Van de Ven Lehrstuhl für Mathematik (Operatoralgebren) (Heisenberg-Professur)

Involved external institutions

Università degli Studi di Trento IT Italy (IT) University of Genova / Università degli Studi di Genova IT Italy (IT)

How to cite

APA:

Drag, N., Pettinar, L., & Van de Ven, C. (2026). Subcriticality at High Temperatures in Spin Lattice Systems. (Unpublished, Submitted).

MLA:

Drag, Nicolò, Lorenzo Pettinar, and Christiaan Van de Ven. Subcriticality at High Temperatures in Spin Lattice Systems. Unpublished, Submitted. 2026.

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