# Quantum spin systems versus Schroedinger operators: A case study in spontaneous symmetry breaking

November 29, 2018

Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but
must physically occur, approximately, before the limit. Approximate SSB has
been independently understood for Schroedinger operators with double well
potential in the classical limit (Jona-Lasinio et al, 1981; Simon, 1985) and
for quantum spin systems in the thermodynamic limit (Anderson, 1952; Tasaki,
2019). We relate these to each other in the context of the Curie-Weiss model,
establishing a remarkable relationship between this model (for finite N) and a
discretized Schroedinger operator with double well potential.

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