We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of inho-mogeneities. For certain choices of the inhomogeneities we study arrow correlation functions on the horizontal line going through the centre. In particular we obt...

For the Bernoulli matching model of the sequence alignment problem we apply the Bethe Ansatz technique via an exact mapping to the five-vertex model on a square lattice. Considering the terracelike representation of the sequence alignment problem, we reproduce by the Bethe Ansatz the results for the averaged length of the longest common subsequence in the Bernoulli approximation. In addition, w...

A metric is introduced on the two dimensional space of parameters describing the Ising model on a Bethe lattice of co-ordination number q. The geometry associated with this metric is analysed and it is shown that the Gaussian curvature diverges at the critical point. For the special case q = 2 the curvature reduces to an already known result for the one dimensional Ising model. The Gaussian cur...

Jacobi polynomials are polynomials whose zeros form the unique solution of the Bethe Ansatz equation associated with two sl2 irreducible modules. We study sequences of r polynomials whose zeros form the unique solution of the Bethe Ansatz equation associated with two highest weight slr+1 irreducible modules, with the restriction that the highest weight of one of the modules is a multiple of the...

Marginal β deformations of N = 4 super-Yang-Mills theory are known to correspond to a certain class of deformations of the S background subspace of type IIB string theory in AdS5 × S. An analogous set of deformations of the AdS5 subspace is reviewed here. String energy spectra computed in the near-pp-wave limit of these backgrounds match predictions encoded by discrete, asymptotic Bethe equatio...

The dilute A 3 model is a solvable IRF (interaction-round-a-face) model with three local states and adjacency conditions encoded by the Dynkin diagram of the Lie algebra A 3. It can be regarded as a solvable version of a critical Ising model in a magnetic eld. One therefore expects the scaling limit to be governed by Zamolod-chikov's integrable perturbation of the c = 1=2 conformal eld theory. ...

In this paper, we address the inverse problem, or the statistical machine learning problem, in Markov random fields with a non-parametric pair-wise energy function with continuous variables. The inverse problem is formulated by maximum likelihood estimation. The exact treatment of maximum likelihood estimation is intractable because of two problems: (1) it includes the evaluation of the partiti...

We present in an unified and detailed way the Nested Bethe Ansatz for closed spin chains based on Y(gl(n)), Y(gl(m|n)), Ûq(gl(n)) or Ûq(gl(m|n)) (super)algebras, with arbitrary representations (i.e. ‘spins’) on each site of the chain. The construction extends and unifies the results already obtained for spin chains based on Y(gl(n)) or Ûq(gl(n)) and for some particular super-spin chains. We giv...

We develop a transfer matrix method to compute exactly the spin-spin correlation functions < s0sn > of Bethe lattice spin models in the external magnetic field h and for any temperature T . We first compute < s0sn > for the most general spin S Ising model, which contains all possible single-ion and nearest-neighbor pair interactions. This general spin S Ising model includes the spin-1/2 simple ...

Recently certain identities for solutions of the Bethe equations in the six-vertex model were obtained in [FM]. In the note we give an elementary proof of similar identities for the case of the inhomogeneous arbitrary spin XXX or XXZ model. Though the corresponding calculations can be done in the elliptic case too, almost without modification , in that case the resulting identites have rather t...