Related papers: Q-colourings of the triangular lattice: Exact expo…
The two-dimensional $Q$-state Potts model with real couplings has a first-order transition for $Q>4$. We study a loop-model realization in which $Q$ is a continuous parameter. This model allows for the collision of a critical and a…
Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically…
We study the P"oschl-Teller equation in complex domain and deduce infinite families of TQ and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms…
We formulate a closed set of equations for the spectrum of two-dimensional bi-scalar fishnet conformal field theory, comprising Baxter equations and quantisation conditions, which we derive operatorially from the underlying sl(2) spin…
We study the chromatic polynomial P_G(q) for m \times n triangular-lattice strips of widths m <= 12_P, 9_F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary…
A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…
We have constructed a one dimensional exactly solvable model, which is based on the t-J model of strongly correlated electrons, but which has additional quantum group symmetry, ensuring the degeneration of states. We use Bethe Ansatz…
Using the principles of the conformal quantum field theory and the finite size corrections of the energy of the ground and various excited states, we calculate the boundary critical exponents of single- and multicomponent Bethe ansatz…
We study the $q$ states Potts model with four site interaction on the square lattice. Based on the asymptotic behaviour of lattice animals, it is argued that when $q\leq 4$ the system exhibits a second-order phase transition, and when $q >…
XXX spin chain with spin $s=-1$ appears as an effective theory of Quantum Chromodynamics. It is equivalent to lattice nonlinear Schroediger's equation: interacting chain of harmonic oscillators [bosonic]. In thermodynamic limit each energy…
We study the chromatic polynomial P_G(q) for m \times n square- and triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the…
We study the phase diagram of the ferromagnetic $q$-state Potts model on the various three-dimensional lattices for integer and non-integer values of $q>1$. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
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…
We study the emergence of non-compact degrees of freedom in the low energy effective theory for a class of $\mathbb{Z}_2$-staggered six-vertex models. In the finite size spectrum of the vertex model this shows up through the appearance of a…
We study the challenging thermal phase transition to stripe order in the frustrated square-lattice Ising model with couplings J1<0 (nearest-neighbor, ferromagnetic) and J2>0 (second-neighbor, antiferromagnetic) for g=J2/|J1|>1/2. Using…
The free energy per lattice site of a quantum spin chain in the thermodynamic limit is determined by a single `dominant' Eigenvalue of an associated quantum transfer matrix in the infinite Trotter number limit. For integrable quantum spin…
We consider the critical behavior of the random q-state Potts model in the large-q limit with different types of disorder leading to either the nonfrustrated random ferromagnet regime or the frustrated spin glass regime. The model is…
The partition function of the Baxter-Wu model is exactly related to the generating function of a site-colouring problem on a hexagonal lattice. We extend the original Bethe ansatz solution of these models in order to obtain the eigenspectra…
A proper $q$-coloring of a graph is an assignment of one of $q$ colors to each vertex of the graph so that adjacent vertices are colored differently. Sample uniformly among all proper $q$-colorings of a large discrete cube in the integer…