Universal Relations for Non Solvable Statistical Models

Abstract

We present the first rigorous derivation of a number of universal relations for a class of models with continuously varying indices (among which are interacting planar Ising models, quantum spin chains and 1D Fermi systems), for which an exact solution is not known, except in a few special cases. Most of these formulas were conjectured by Luther and Peschel, Kadanoff, Haldane, but only checked in the special solvable models; one of them, related to the anisotropic Ashkin-Teller model, is novel.

4 pages, no figure, letter

References in corpus (4)

• Universal theory of nonlinear Luttinger liquids
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

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• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
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• Energy correlations of non-integrable Ising models: The scaling limit in the cylinder
• Spin Hall insulators beyond the Helical Luttinger model
• Universal finite size corrections and the central charge in non solvable Ising models
• Drude weight in non solvable quantum spin chains
• Dense gaps and scaling relations in the interacting Aubry-Andre' model
• Anomalous behavior in an effective model of graphene with Coulomb interactions
• Anomaly cancellation condition in an effective non-perturbative electroweak theory
• Quantum Quench for inhomogeneous states in the non-local Luttinger model
• Emergent Adler-Bardeen theorem
• Height fluctuations in non-integrable classical dimers
• Interacting Fermions Picture for Dimer Models
• Non-integrable dimer models: universality and scaling relations
• Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance
• Universal Luttinger Liquid Relations in the 1D Hubbard Model
• Universality of charge transport in weakly interacting fermionic systems
• Non-integrable fermionic chains near criticality
• Quantum Hall conductivity in the presence of interactions