Massive and massless phases in self-dual $Z_N$ spin models: some exact results from the thermodynamic Bethe ansatz

Abstract

The generally accepted phase diagrams for the discrete $Z_N$ spin models in two dimensions imply the existence of certain renormalisation group flows, both between conformal field theories and into a massive phase. Integral equations are proposed to describe these flows, and some properties of their solutions are discussed. The infrared behaviour in massless and massive directions is analysed in detail, and the techniques used are applied to a number of other models.

64 pages, latex, 4 eps files, uses epsf.tex. References added and typos corrected; version to appear in Nuclear Physics B

References in corpus (21)

• Dynkin TBA's
• Fermionic Sum Representations for Conformal Field Theory Characters
• Painleve III and 2D Polymers
• Universal Properties of Self-Avoiding Walks from Two-Dimensional Field Theory
• Scattering and Thermodynamics of Integrable N=2 Theories
• Dilogarithm Identities in Conformal Field Theory
• Massless Flows II: the exact S-matrix approach
• Root Systems and Purely Elastic S-Matrices II
• Spectra in Conformal Field Theories from the Rogers Dilogarithm
• Massless Flows I: the sine-Gordon and O(n) models
• Thermodynamic Bethe Ansatz for G_k x G_l / G_{k+l} Coset Models Perturbed by Their ϕ_{1,1,Adj} Operator
• ADE functional dilogarithm identities and integrable models
• The Sine-Gordon Model as $\SO(n)_{1} \times \SO(n)_{1} \over \SO(n)_{2}$ Perturbed Coset Theory and Generalizations
• Graphs and Reflection Groups
• Integrable perturbations of CFT with complex parameter: the $M_{3/5}$ model and its generalizations
• Partition Functions, Intertwiners and the Coxeter Element
• The thermodynamic Bethe ansatz for deformed W$A_{N-1}$ conformal field theories
• New functional dilogarithm identities and sine-Gordon Y-systems
• Infrared Behaviour of Massless Integrable Flows entering the Minimal Models from phi_31
• Fateev-Zamolodchikov spin chain: excitation spectrum, completeness and thermodynamics
• Tunneling and Energy Splitting in Ising Models

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