Related papers: Star-Triangle Relation for a Three Dimensional Mod…
We obtain the exact physical characteristics of the triple-chain Ising model on a torus with all possible multispin interactions invariant with respect to rotation by the angle $2\pi / 3$. The exact value of the partition function in a…
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…
We study a model of a semiflexible long chain polymer confined to a two-dimensional slit of width $w$, and interacting with the walls of the slit. The interactions with the walls are controlled by Boltzmann weights $a$ and $b$, and the…
We calculate the partition function of the $q$-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values…
The normalization factor in the star-triangle relation can be evaluated in a simple form by taking determinants. If we combine this with the rotation symmetries, then we can show that a certain simple quantity $I$ has to be independent of…
A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on $\mathbb{Z}^3$ is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter…
As is known, tetrahedron equations lead to the commuting family of transfer-matrices and provide the integrability of corresponding three-dimensional lattice models. We present the modified version of these equations which give the…
We investigate the dynamical superlattice correlation in the two-dimensional three-band Hubbard model on the basis of the unrestricted fluctuation exchange approximation. We calculate the one-particle spectral function, the spin correlation…
Based on the spectrum identified in our earlier work [arXiv:1809.02191], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the $Q$-state Potts model. Crucial in our…
We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group $G$. When $G=SU(2)$, the statistical weight is constructed from the $15j$-symbol as well as the $6j$-symbol for recombination of…
We analyze the partition function of the dimer model on an $\mathcal{M} \times \mathcal{N}$ triangular lattice wrapped on torus obtained by Fendley, Moessner and Sondhi [Phys. Rev. B \textbf{66}, 214513 (2002)]. From a finite-size analysis…
Chiral spin liquids (CSLs) are exotic phases of interacting spins in two dimensions, characterized by long-range entanglement and fractional excitations. We construct a local Hamiltonian on the triangular lattice that stabilizes the…
Starting from a Calogero--Sutherland model with hyperbolic interaction confined by an external field with Morse potential we construct a Heisenberg spin chain with exchange interaction $\propto 1/\sinh^2 x$ on a lattice given in terms of…
The three-state antiferromagnetic Potts model on the simple cubic lattice is investigated using the cluster variation method in the cube and the star-cube approximations. The broken-sublattice-symmetry phase is found to be stable in the…
Duality relations for the 2D nonhomogeneous Ising model on the finite square lattice wrapped on the torus are obtained. The partition function of the model on the dual lattice with arbitrary combinations of the periodical and antiperiodical…
Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier…
We compute the partition function of the Potts model with arbitrary values of $q$ and temperature on some strip lattices. We consider strips of width $L_y=2$, for three different lattices: square, diced and `shortest-path' (to be defined in…
A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest neighbor interactions, the vertices defining the model also interact alongone of the diagonals of the lattice. Such family of…
We report progress in constructing Boltzmann weights for integrable 3-dimensional lattice spin models. We show that a large class of vertex solutions to the modified tetrahedron equation can be conveniently parameterized in terms of N-th…
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…