We prove the existence of a stable solution of the renormalized fixed point equation for the distribution of the single-site magnetization in the Bethe lattice spin glass at zero temperature. The proof is computer assisted. RESUME. Nous prouvons 1’existence d’une solution stable de l’équation de point fixe de renormalisation pour la distribution de la magnétisation d’un spin dans Ie modele de v...

A t− J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra gl(2|1). PACS: 03.65.Fd, 05.50+q, 71.20.Ad

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . 1.1 Markov Random Field Models 1 1.2 An Overview of Optimal Estimators and Approximations . . . . . . . 2 1.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 Goa...

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 spin1 2 simple Ising...

An exactly integrable symplectic correspondence is derived which in a continuum limit leads to the equations of motion of the relativistic generalization of the Calogero-Moser system, that was introduced for the first time by Ruijsenaars and Schneider. For the discrete-time model the equations of motion take the form of Bethe Ansatz equations for the inhomogeneous spin– 1 2 Heisenberg magnet. W...

We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving...

On the Algebraic Bethe Ansatz for XXX spin chain: creation operators " beyond the equator ". Abstract Considering the XXX spin-1/2 chain in the framework of the Algebraic Bethe Ansatz (ABA) we make the following short comment: the product of the creation operators corresponding to the recently found solution of the Bethe equations " on the wrong side of the equator " [1] is just zero (not only ...

We solve, by means of a nested coordinate Bethe ansatz, the open-boundaries scattering theory describing the excitations of a free open string propagating in AdS5 × S, carrying large angular momentum J = J56, and ending on a maximal giant graviton whose angular momentum is in the same plane. We thus obtain the all-loop Bethe equations describing the spectrum, for J finite but large, of the ener...

We review the main result of cond-mat/0503564. The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the sl2 loop algebra symmetry if the q parameter is given by a root of unity, q 0 = 1, for an integer N . We discuss the dimensions of the degenerate eigenspace generated by a regular Bethe state in some sectors, rigorously as follows: We show that every regul...

We apply the Bethe-Peierls approximation to the problem of the inverse Ising model and show how the linear response relation leads to a simple method to reconstruct couplings and fields of the Ising model. This reconstruction is exact on tree graphs, yet its computational expense is comparable to other mean-field methods. We compare the performance of this method to the independent-pair, naive ...