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.
Ground States in Non-relativistic Quantum Electrodynamics
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The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the Schr\"odinger equation. We prove quite generally that this state exists for {\it all values} of the fine-structure constant and ultraviolet cutoff. We also show the same thing for a many-particle system under physically natural conditions.
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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.