Renormalization group pathologies and the definition of Gibbs states

Bricmont, Jean;Kupiainen, Antti;Lefevere, R.
(1998) Communications in Mathematical Physics — Vol. 194, n° 2, p. 359-388 (1998)

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Authors
  • Bricmont, JeanUCLouvain
    Author
  • Kupiainen, AnttiUCLouvain
    Author
  • Lefevere, R.
    Author
Abstract
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.
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Bricmont, J., Kupiainen, A., & Lefevere, R. (1998). Renormalization group pathologies and the definition of Gibbs states. Communications in Mathematical Physics, 194(2), 359-388. https://doi.org/10.1007/s002200050362 (Original work published 1998)