Existence of Ground States in the Infrared-Critial Spin Boson Model Hinrichs, Benjamin Hiroshima, Fumio 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. 2022 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://ris.uni-paderborn.de/record/43496 Hinrichs B. Existence of Ground States in the Infrared-Critial Spin Boson Model. In: Hiroshima F, ed. <i>Mathematical Aspects of Quantum Fields and Related Topics</i>. Vol 2235. RIMS Kôkyûroku. ; 2022:60-73. eng info:eu-repo/semantics/altIdentifier/arxiv/2204.00287 info:eu-repo/semantics/openAccess