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In this work we have developed the essential tools for the algebraic Bethe ansatz solution of integrable vertex models invariant by a unique U(1) charge symmetry. The formulation is valid for arbitrary statistical weights and respective…

Mathematical Physics · Physics 2009-11-13 C. S. Melo , M. J. Martins

The partition function of the six-vertex model on a square lattice with domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix model or a discretized version of it (similar to sums over Young diagrams), depending on…

Mathematical Physics · Physics 2009-10-31 P. Zinn-Justin

The Bethe ansatz equation is solved to obtain analytically the leading finite-size correction of the spectra of the asymmetric XXZ chain and the accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary at zero…

Statistical Mechanics · Physics 2009-10-28 Doochul Kim

Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for…

Combinatorics · Mathematics 2007-05-23 Graham R. Brightwell , Peter Winkler

We consider the $L$-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer…

Condensed Matter · Physics 2009-10-28 Y K Zhou , M T Batchelor

We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum…

Mathematical Physics · Physics 2024-06-17 Filippo Colomo , Giuseppe Di Giulio , Andrei G. Pronko

We decorate the square lattice with two species of polygons under the constraint that every lattice edge is covered by only one polygon and every vertex is visited by both types of polygons. We end up with a 24 vertex model which is known…

Statistical Mechanics · Physics 2009-11-10 David Dei Cont , Bernard Nienhuis

Applying a unifying Lax operator approach to statistical systems a new class of integrable vertex models based on quantum algebra is proposed, which exhibits a rich variety for generic q, q roots of unity and q -> 1. Exact solutions are…

Condensed Matter · Physics 2009-11-07 Anjan Kundu

In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term ``stochastic symplectic ice''. The models consist of alternating rows of two types of vertices. The…

Mathematical Physics · Physics 2022-06-22 Chenyang Zhong

A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice $\mathcal N=2$ supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified.…

Statistical Mechanics · Physics 2014-12-04 Christian Hagendorf , Thessa B. Fokkema , Liza Huijse

We apply the algebraic Bethe ansatz developed in our previous paper \cite{CM} to three different families of U(1) integrable vertex models with arbitrary $N$ bond states. These statistical mechanics systems are based on the higher spin…

Mathematical Physics · Physics 2009-08-03 M. J. Martins , C. S. Melo

We study the solutions of the Yang-Baxter equation associated to nineteen vertex models invariant by the parity-time symmetry from the perspective of algebraic geometry. We determine the form of the algebraic curves constraining the…

Mathematical Physics · Physics 2011-02-09 R. A. Pimenta , M. J. Martins

We perform a numerical study of the F-model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size…

Statistical Mechanics · Physics 2017-05-17 Rick Keesman , Jules Lamers

The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as…

Mathematical Physics · Physics 2021-03-17 Vladimir V. Bazhanov , Gleb A. Kotousov , Sergii M. Koval , Sergei L. Lukyanov

The procedure for obtaining integrable vertex models via reflection matrices on the square lattice with open boundaries is reviewed and explicitly carried out for a number of two- and three-state vertex models. These models include the…

High Energy Physics - Theory · Physics 2010-04-08 C. M. Yung , M. T. Batchelor

The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2 grading along both chain and time directions is presented. The XXZ model with staggered disposition along a chain of both, the anisotropy \pm\Delta, as well as…

High Energy Physics - Theory · Physics 2007-05-23 D. Arnaudon , R. Poghossian , A. Sedrakyan , P. Sorba

Quantum systems on a one-dimensional lattice are ubiquitous in the study of models exactly-solved by Bethe Ansatz techniques. Here it is shown that including global-range interaction opens scope for Bethe Ansatz solutions that are not…

Exactly Solvable and Integrable Systems · Physics 2026-01-01 Jon Links

An exactly solvable lattice model with infinite-range potential is applied to uniaxial ferroelectrics. Asymptotically exact expression for free energy as a function of an order parameter at any temperatures is obtained. Effect of thermal…

Materials Science · Physics 2011-05-06 A. Yu. Zakharov , M. I. Bichurin , N. V. Evstigneeva

Starting from the fusion rules for the algebra $SO(5)_2$ we construct one-dimensional lattice models of interacting anyons with commuting transfer matrices of `interactions round the face' (IRF) type. The conserved topological charges of…

Strongly Correlated Electrons · Physics 2014-11-04 Peter E. Finch , Michael Flohr , Holger Frahm

We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to…

Mathematical Physics · Physics 2017-06-28 Rouven Frassek