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First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…

High Energy Physics - Theory · Physics 2007-05-23 Alexander Ushveridze

We find and analyse the exact solution of a model of three different polymers with asymmetric contact interactions in two dimensions, modelling a scenario where there are different types of polymers involved. In particular, we find the…

Statistical Mechanics · Physics 2025-09-15 Aleksander L Owczarek , Andrew Rechnitzer

We introduce a spin-1/2 model in three dimensions which is a generalization of the well-known Kitaev model on a honeycomb lattice. Following Kitaev, we solve the model exactly by mapping it to a theory of non-interacting fermions in the…

Mesoscale and Nanoscale Physics · Physics 2013-05-29 Saptarshi Mandal , Naveen Surendran

We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock space, we prove a Cauchy identity for…

Combinatorics · Mathematics 2022-01-04 Michael J. Curran , Claire Frechette , Calvin Yost-Wolff , Sylvester W. Zhang , Valerie Zhang

A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated…

Statistical Mechanics · Physics 2009-10-31 Alain Verberkmoes , Bernard Nienhuis

We present a set of polynomial equations that provides models of the lattice Boltzmann theory for any required level of accuracy and for any dimensional space in a general form. We explicitly derive two- and three-dimensional models…

Mathematical Physics · Physics 2015-05-28 Jae Wan Shim

We introduce in this paper an exact solvable BCS-Hubbard model in arbitrary dimensions. The model describes a p-wave BCS superconductor with equal spin pairing moving on a bipartite (cubic, square etc.) lattice with on site Hubbard…

Strongly Correlated Electrons · Physics 2018-01-31 Zewei Chen , Xiaohui Li , Tai Kai Ng

The general d-dimensional twisted group lattice is solved. The irreducible representations of the corresponding group are constructed by an explicit procedure. It is proven that they are complete. All matrix representation solutions to the…

High Energy Physics - Theory · Physics 2009-10-28 O. Lechtenfeld , S. Samuel

There is no an exact solution to three-dimensional (3D) finite-size Ising model (referred to as the Ising model hereafter for simplicity) and even two-dimensional (2D) Ising model with non-zero external field to our knowledge. Here by using…

General Physics · Physics 2018-10-12 Rong Qiang Wei

A closed-form exact analytical solution for the q-state Potts model on a ladder 2 x oo with arbitrary two-, three-, and four-site interactions in a unit cell is presented. Using the obtained solution it is shown that the finite-size…

Statistical Mechanics · Physics 2009-11-07 M. A. Yurishchev

In the past decade, tremendous efforts have been made towards understanding fermionic symmetry protected topological (FSPT) phases in interacting systems. Nevertheless, for systems with continuum symmetry, e.g., electronic insulators, it is…

Strongly Correlated Electrons · Physics 2023-09-12 Qing-Rui Wang , Yang Qi , Chen Fang , Meng Cheng , Zheng-Cheng Gu

Nonperturbative exact solutions are allowed for quantum integrable models in one space-dimension. Going beyond this class we propose an alternative Lax matrix approach, exploiting the hidden multi-time concept in integrable systems and…

High Energy Physics - Theory · Physics 2016-05-18 Anjan Kundu

We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algorithms solve the two problems in any fixed dimension d in the…

Metric Geometry · Mathematics 2007-05-23 Achill Schuermann , Frank Vallentin

Exact loop-variables formulation of pure gauge lattice QCD_3 is derived from the Wilson version of the model. The observation is made that the resulting model is two-dimensional. This significant feature is shown to be a unique property of…

High Energy Physics - Theory · Physics 2009-10-30 B. Rusakov

By defining a graded global R-operator $\mathbb{R}_{ab}^{(2D,2S)}$ that couples free-fermion structures and incorporates anisotropic Hubbard interactions while satisfying the Yang--Baxter equation, we construct a strictly solvable…

Exactly Solvable and Integrable Systems · Physics 2025-12-09 Ze Tao , Fujun Liu

Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer…

Statistical Mechanics · Physics 2009-10-30 V. Popkov , Doochul Kim , H. Y. Huang , F. Y. Wu

This paper describes a lattice version of the Skyrme model in 2+1 and 3+1 dimensions. The discrete model is derived from a consistent discretization of the radial continuum problem. Subsequently, the existence and stability of the skyrmion…

Exactly Solvable and Integrable Systems · Physics 2008-12-18 Theodora Ioannidou , Panos Kevrekidis

We present a generic and systematic approach for constructing D-dimensional lattice models with exactly solvable d-dimensional boundary states localized to corners, edges, hinges and surfaces. These solvable models represent a class of…

Mesoscale and Nanoscale Physics · Physics 2019-02-20 Flore K. Kunst , Guido van Miert , Emil J. Bergholtz

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearising transform which…

Exactly Solvable and Integrable Systems · Physics 2017-06-29 Wei Fu , Frank Nijhoff

We develop the method based on $ \mathcal{B} $-automorphism for finding new lattice integrable models with various dimensions of local Hilbert spaces. We initiate the technique by implementing it to the two-dimensional models and resolve…

High Energy Physics - Theory · Physics 2023-12-07 Anton Pribytok