Related papers: 3-Dimensional Multilayered 6-vertex Statistical Mo…
In this paper, we review a few known facts on the coordinate Bethe ansatz. We present a detailed construction of the Bethe ansatz vector $\psi$ and energy $\Lambda$, which satisfy $V \psi = \Lambda \psi$, where $V$ is the the transfer…
The lattice spin model with $Q$--component discrete spin variables restricted to have orientations orthogonal to the faces of $Q$-dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The…
The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches…
We present an infinite-dimensional lattice of two-by-two plaquettes, the quadruple Bethe lattice, with Hubbard interaction and solve it exactly by means of the cluster dynamical mean-field theory. It exhibits a $d$-wave superconducting…
The exact solution of a quantum Bethe lattice model in the thermodynamic limit amounts to solve a functional self-consistent equation. In this paper we obtain this equation for the Bose-Hubbard model on the Bethe lattice, under two…
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…
We computed the phase diagram for a system of model anisotropic particles with six attractive patches in an octahedral arrangement. We chose to study this model for a relatively narrow value of the patch width where the lowest-energy…
We consider the quark--anti-quark potential on the three sphere or the generalized cusp anomalous dimension in planar N=4 SYM. We concentrate on the vacuum potential in the near BPS limit with $L$ units of R-charge. Equivalently, we study…
The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the 2-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-axis limit, two finite temperature vortex unbinding transitions have been…
This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the…
We study the classical cubic-lattice double dimer model, consisting of two coupled replicas of the close-packed dimer model, using a combination of theoretical arguments and Monte Carlo simulations. Our results establish the presence of a…
Systems of charged particles on anisotropic three-dimensional lattices are investigated theoretically using Debye-Huckel theory. It is found that the thermodynamics of these systems strongly depends on the degree of anisotropy. For weakly…
We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell,…
Changing the variables in the Bethe Ansatz Equations (BAE) for the XXZ six-vertex model we had obtained a coupled system of polynomial equations. This provided a direct link between the BAE deduced from the Algebraic Bethe Ansatz (ABA) and…
In this paper we present numerical analysis of the phase transition of the area-interaction model, which is a standard model of Statistical Mechanics. The theoretical results are based on a recent paper by Dereudre \& Houdebert…
Engineering quantum phases with spontaneously broken symmetries is a major goal of research in different fields. Trapped ultracold Rydberg-excited atoms in optical lattices are a promising platform for realizing quantum phases with broken…
We present the exact Bethe ansatz solution for the two-dimensional BCS pairing Hamiltonian with p_x + i p_y symmetry. Using both mean-field theory and the exact solution we obtain the ground-state phase diagram parameterized by the filling…
In this paper we continue the study of the three-layer Zamolodchikov model started in our previous works. We analyse numerically the solutions to the Bethe ansatz equations. We consider two regimes I and II which differ by the signs of the…
We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice…
We devise a generic recipe for constructing $D$-dimensional lattice models whose $d$-dimensional boundary states, located on surfaces, hinges, corners, and so forth, can be obtained exactly. The solvability is rooted in the underlying…