On the S-matrix of the Sub-leading Magnetic Deformation of the Tricritical Ising Model in Two Dimensions

We compute the $S$-matrix of the Tricritical Ising Model perturbed by the subleading magnetic operator using Smirnov's RSOS reduction of the Izergin-Korepin model. The massive model contains kink excitations which interpolate between two degenerate asymmetric vacua. As a consequence of the different structure of the two vacua, the crossing symmetry is implemented in a non-trivial way. We use finite-size techniques to compare our results with the numerical data obtained by the Truncated Conformal Space Approach and find good agreement.Comment: 21 page

Algebraic arctic curves in the domain-wall six-vertex model

The arctic curve, i.e. the spatial curve separating ordered (or `frozen') and disordered (or `temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root-of-unity vertex weights. In these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve. Some interesting examples are discussed in detail. The upper bound on the maximal degree of the equation in a generic root-of-unity case is obtained.Comment: 15 pages, no figures; v2: metadata correcte

Counting non-planar diagrams: an exact formula

Abstract We present an explicit solution of a simply stated, yet unsolved, combinatorial problem, of interest both in quantum field theory (Feynman diagrams enumeration, beyond the planar approximation) and in statistical mechanics (high temperature loop expansion of some frustrated lattice spin model)

Temperature correlators in the two-component one-dimensional gas

The quantum nonrelativistic two-component Bose and Fermi gases with the infinitely strong point-like coupling between particles in one space dimension are considered. Time and temperature dependent correlation functions are represented in the thermodynamic limit as Fredholm determinants of integrable linear integral operators.Comment: 40 pages, LaTeX, a4.st