2009/11/16 by Yacine Ikhlef, Jesper Lykke Jacobsen, Hubert Saleur · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Anisotropy #Ansatz #Bethe ansatz #Black Holes and Theoretical Physics #Central charge #Combinatorics #Conformal field theory #Conformal map #Fermion #Integrable system #Ising model #Lattice (music) #MAJORANA #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Square lattice #Vertex (graph theory) #Vertex model #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/43/22/225201
published as J. Phys. A 43, 225201 (2010) · 38 pages, 14 figures, 3 appendices
arxiv created 2009/11/16 · openalex publication_date 2010/05/11 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
New solvable vertex models can be easily obtained by staggering the spectral parameter in already known ones. This simple construction reveals some surprises: for appropriate values of the staggering, highly non-trivial continuum limits can be obtained. The simplest case of staggering with period 2 (the case) for the six-vertex model was shown to be related, in one regime of the spectral parameter, to the critical antiferromagnetic Potts model on the square lattice, and has a non-compact continuum limit. Here we study the other regime: in the very anisotropic limit, it can be viewed as a zig–zag spin chain with spin anisotropy. From the Bethe–Ansatz solution, we obtain the central charge c = 2, the conformal spectrum and the continuum partition function, corresponding to one free boson and two Majorana fermions. Finally, moving in more physical territory, we obtain a massive integrable deformation of the model on the lattice. Interestingly, its scattering theory is a massive version of the one for the flow between minimal models. The corresponding field theory is argued to be a complex version of the C (2) 2 Toda theory.