We present the exact solution of the Osp(1|2) invariant magnet by the Bethe ansatz approach. The associated Bethe ansatz equation exhibit a new feature by presenting an explicit and distinct phase behaviour in even and odd sectors of the theory. The ground state, the low-lying excitations and the critical properties are discussed by exploiting the Bethe ansatz solution.

The Bethe ansatz can be used to compute anomalous dimensions in N = 4 SYM theory. The classical solutions of the sigma-model on AdS5 × S 5 can also be parameterized by an integral equation of Bethe type. In this note the relationship between the two Bethe ansätze is reviewed following hep-th/0402207.

We discuss the states which contribute in the thermodynamic limit of the mirror theory, the latter is obtained from the light-cone gauge-fixed string theory in the AdS5×S background by the double-Wick rotation. We analyze the Bethe-Yang equations for the mirror theory and formulate the string hypothesis. We show that in the thermodynamic limit solutions of the Bethe-Yang equations arrange thems...

An exact solution of the model of fully packed loops of two colors on a square lattice has recently been proposed by Dei Cont and Nienhuis using the coordinate Bethe Ansatz approach. We point out here a simpler alternative, in which the transfer matrix is directly identified as a product of R-matrices; this allows to apply the (nested) algebraic Bethe Ansatz, which leads to the same Bethe equat...

The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary conditions. The method discussed here for solving the Bethe-Salpeter equation requires only that the equation can be Wick rotated and that the two angular v...

The Bethe approximation, discovered in statistical physics, gives an efficient algorithm called belief propagation (BP) for approximating a partition function. BP empirically gives an accurate approximation for many problems, e.g., low-density parity-check codes, compressed sensing, etc. Recently, Vontobel gives a novel characterization of the Bethe approximation using graph cover. In this pape...

The Asymmetric Simple Exclusion Process (ASEP) plays the role of a paradigm in NonEquilibrium Statistical Mechanics. We review exact results for the ASEP obtained by Bethe Ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov Matrix of the ASEP are derived from the algebraic Bethe Ansatz. Using these equations we explain how to ...

For undirected graphical models, belief propagation often performs remarkably well for approximate marginal inference, and may be viewed as a heuristic to minimize the Bethe free energy. Focusing on binary pairwise models, we demonstrate that several recent results on the Bethe approximation may be generalized to a broad family of related pairwise free energy approximations with arbitrary count...

Functional relations and nested Bethe ansatz for sl(3) chiral Potts model at q 2 = −1. Abstract We obtain the functional relations for the eigenvalues of the transfer matrix of the sl(3) chiral Potts model for q 2 = −1. For the homogeneous model in both directions a solution of these functional relations can be written in terms of roots of Bethe ansatz-like equations. In addition , a direct nes...