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Correlation Bound for a One-Dimensional Continuous Long-Range Ising Model

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arxiv 2104.03013 v1 pith:GI3IDIBH submitted 2021-04-07 math-ph math.MP

David Hasler , Benjamin Hinrichs , Oliver Siebert This is my paper · ORCID
classification math-phmath.MP
keywords modelboundcorrelationisinglong-rangemagneticmeasureone-dimensional
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abstract

We consider a measure given as the continuum limit of a one-dimensional Ising model with long-range translationally invariant interactions. Mathematically, the measure can be described by a self-interacting Poisson driven jump process. We prove a correlation inequality, estimating the magnetic susceptibility of this model, which holds for small $L^1$-norm of the interaction function. The bound on the magnetic susceptibility has applications in quantum field theory and can be used to prove existence of ground states for the spin boson model.

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Cited by 1 Pith paper

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  1. On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model

    math-ph 2025-01 conditional novelty 8.0 of 10

    Infrared-divergent spin boson model loses its ground state above a finite critical coupling, proved via long range order in a dual continuum Ising model.

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