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Low temperature properties for correlation functions in classical $$N$$-vector spin models. (English) Zbl 0932.81024
In the framework of the $$d\geq 3$$ dimensional ferromagnetic lattice model $$SO(N)$$-symmetry-breaking mechanism is investigated. The model contains the isotropic nearest-neighbour ferromagnetic interactions; a Goldstone-like term and an explicit symmetry-breaking term are introduced. In the suitably defined low-temperature limit and vanishing symmetry breaking, the appearance of a single pure ferromagnetic state is proved. The decay of the correlation functions as inverse of the separation distance’s power is proved. In particular, the decay of the transverse mode correlation agrees with the Goldstone theorem.

##### MSC:
 81T25 Quantum field theory on lattices 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 46N50 Applications of functional analysis in quantum physics 81R40 Symmetry breaking in quantum theory
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