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Extended Scaling Relations for Planar Lattice Models

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Abstract

It is widely believed that the critical properties of several planar lattice systems, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective continuum fermionic theory obtained as a formal scaling limit. On the basis of this assumption several extended scaling relations among their indices were conjectured. We prove the validity of some of them, among which the ones predicted by Kadanoff (Phys Rev Lett 39:903–905, 1977) and by Luther and Peschel (Phys Rev B 12:3908–3917, 1975).

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica, 00133, Roma, Italy

    G. Benfatto & V. Mastropietro

  2. Mathematics Department, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    P. Falco

Authors
  1. G. Benfatto
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  2. P. Falco
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  3. V. Mastropietro
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Correspondence to V. Mastropietro.

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Communicated by G. Gallavotti

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Benfatto, G., Falco, P. & Mastropietro, V. Extended Scaling Relations for Planar Lattice Models. Commun. Math. Phys. 292, 569–605 (2009). https://doi.org/10.1007/s00220-009-0888-z

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  • DOI: https://doi.org/10.1007/s00220-009-0888-z

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