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.
Correlation Bound for a One-Dimensional Continuous Long-Range Ising Model
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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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On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model
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.