The thermodynamic Bethe ansatz is applied to a quantum integrable spin chain associated with the Lie superalgebra osp(1|2). Using the string hypothesis, we derive a set of infinite number of non-linear integral equations (thermodynamic Bethe ansatz equation), which characterize the free energy. The low temperature limit of the free energy is also discussed. Modern Physics Letters A, in press. S...

In this introductory review we discuss dynamical tests of the AdS5 × S5 string/[Formula: see text] Super Yang-Mills duality. After a brief introduction to AdS/CFT, we argue that semiclassical string energies yield information on the quantum spectrum of the string in the limit of large angular momenta on the S5. The energies of the folded and circular spinning string solutions rotating on a S3 w...

A simple method, previously used to calculate the equilibrium concentration of dimers adsorbed on a Bethe lattice as a function of the dimer activity, is generalized to solve the problem of a Bethe lattice in contact with a reservoir containing a mixture of molecules. The molecules may have arbitrary sizes and shapes consistent with the geometry of the lattice and the molecules do not interact ...

We consider the operators with highest anomalous dimension ∆ in the compact rank-one sectors su(1|1) and su(2) of N = 4 super Yang-Mills. We study the flow of ∆ from weak to strong ’t Hooft coupling λ by solving (i) the all-loop gauge Bethe Ansatz, (ii) the quantum string Bethe Ansatz. The two calculations are carefully compared in the strong coupling limit and exhibit different exponents ν in ...

It was recently proved using graph covers (Ruozzi, 2012) that the Bethe partition function is upper bounded by the true partition function for a binary pairwise model that is attractive. Here we provide a new, arguably simpler proof from first principles. We make use of the idea of clamping a variable to a particular value. For an attractive model, we show that summing over the Bethe partition ...

We study the reflection of magnons from a D5-brane in the framework of the AdS/CFT correspondence. We consider two possible orientations of the D5-brane with respect to the reference vacuum state, namely vacuum states aligned along “vertical” and “horizontal” directions. We show that the reflections are of the achiral type. We also show that the reflection matrices satisfy the boundary Yang-Bax...

We study a family of power series characterized by a system of recursion relations (Q-system) with a certain convergence property. We show that the coefficients of the series are expressed by the numbers which formally count the off-diagonal solutions of the Uq(X (1) n ) Bethe equation at q = 0. The series are conjectured to be the Xn-characters of a certain family of irreducible finite-dimensi...

We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T , and study the existence of the free energy density φ, the limit of the log-partition function divided by the number of vertices n as n tends to infinity. We provide a new interpolation scheme and use it to prove existence of, and to explicitly compute, the quantity φ su...

It is shown that an extended q-deformed su(2) algebra with an extra (“Schwinger ”) term can describe Bloch electrons in a uniform magnetic field with an additional periodic potential. This is a generalization of the analysis of Bloch electrons by Wiegmann and Zabrodin. By using a representation theory of this q-deformed algebra, we obtain functional Bethe ansatz equations whose solutions should...

Bethe potentials were introduced by Bethe in 1928 to reduce the size of the dynamical matrix in electron scattering problems using first order perturbation theory [1]. The standard approach is to start from the dynamical equations in the Bloch wave representation, and split the set of diffracted beams into two subsets, namely strong and weak beams, according to some appropriate criterion. While...