2005/12/02 by Jesper Lykke Jacobsen, Hubert Saleur · 5 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2006.02.041
published as Nucl.Phys.B743:207-248,2006
arxiv created 2005/12/02 · openalex publication_date 2006/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We solve the antiferromagnetic transition for the Q-state Potts model (defined geometrically for Q generic) on the square lattice. The solution is based on a detailed analysis of the Bethe ansatz equations (which involve staggered source terms) and on extensive numerical diagonalization of transfer matrices. It involves subtle distinctions between the loop/cluster version of the model, and the associated RSOS and (twisted) vertex models. The latter's continuum limit involves two bosons, one which is compact and twisted, and the other which is not, with a total central charge c=2-6/t, for sqrt(Q)=2cos(pi/t). The non-compact boson contributes a continuum component to the spectrum of critical exponents. For Q generic, these properties are shared by the Potts model. For Q a Beraha number [Q = 4 cos2(pi/n) with n integer] the two-boson theory is truncated and becomes essentially Z_n-2 parafermions. Moreover, the vertex model, and, for Q generic, the Potts model, exhibit a first-order critical point on the transition line, i.e., the critical point is also the locus of level crossings where the derivatives of the free energy are discontinuous. In that sense, the thermal exponent of the Potts model is generically nu=1/2. Things are profoundly different for Q a Beraha number, where the transition is second order, with nu=(t-2)/2 determined by the psi_1 parafermion. As one enters the adjacant Berker-Kadanoff phase, the model flows, for t odd, to a minimal model of CFT with c=1-6/t(t-1), while for t even it becomes massive. This provides a physical realization of a flow conjectured by Fateev and Zamolodchikov in the context of Z_N integrable perturbations. Finally, we argue that the antiferromagnetic transition occurs as well on other two-dimensional lattices.