Infrared bounds, phase transitions and continuous symmetry breaking

@article{Frhlich1976InfraredBP,
  title={Infrared bounds, phase transitions and continuous symmetry breaking},
  author={J{\"u}rg Fr{\"o}hlich and Barry Simon and Thomas J. Spencer},
  journal={Communications in Mathematical Physics},
  year={1976},
  volume={50},
  pages={79-95}
}
We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (φ·φ)32 quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions. The central element of the proof is that for fixed ferromagnetic nearest neighbor coupling, the absolutely continuous part of the two point function ink space is bounded by 0(k−2). When applicable, our results can be fairly accurate numerically. For example… 

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