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A low temperature expansion for classical \(N\)-vector models. I: A renormalization group flow. (English) Zbl 0811.60100

Summary: A class of low temperature lattice classical spin models with a symmetry group \(O(N)\) is considered, including the classical Heisenberg model. A renormalization group approach in a small field approximation is formulated and studied, with a goal to prove the so-called “spin-wave picture” displaying massless behavior of the models.

MSC:

60K40 Other physical applications of random processes
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
81T25 Quantum field theory on lattices
81T17 Renormalization group methods applied to problems in quantum field theory
82B28 Renormalization group methods in equilibrium statistical mechanics
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