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Renormalization group pathologies and the definition of Gibbs states. (English) Zbl 0914.60089
Summary: We show that the so-called renormalization group pathologies in low temperature Ising models are due to the fact that the renormalized Hamiltonian is defined only almost everywhere (with respect to the renormalized Gibbs measures). We construct this renormalized Hamiltonian using a renormalization group method developed for random systems and we show that the pathologies are analogous to Griffiths’ singularities.

MSC:
60K40 Other physical applications of random processes
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B28 Renormalization group methods in equilibrium statistical mechanics
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