  We review recent results on the existence of ground states for the
infrared-critical spin boson model, which describes the interaction of a
massless bosonic field with a two-state quantum system. Explicitly, we derive a
critical coupling $\lambda_{\mathsf c}>0$ such that the spin boson model
exhibits a ground state for coupling constants $\lambda$ with
$|\lambda|<\lambda_{\mathsf c}$. The proof combines a Feynman-Kac-Nelson
formula for the spin boson model with external magnetic field, a 1D-Ising model
correlation bound and a compactness argument in Fock space. Elaborating on the
connection to a long-range 1D-Ising model, we briefly discuss the conjecture
that the spin boson model does not have a ground state at large coupling. This
note is based on joint work with David Hasler and Oliver Siebert.
