An exact solution on the ferromagnetic Face-Cubic spin model on a Bethe lattice

We investigate the quantum phase diagram of the exactly solved mixed spin-(1/2,1) ladder via the thermodynamic Bethe ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases associated with su(2), su(4) and su(6) symmetries. In the presence of a strong magnetic field, there is a third and full saturation magnetization plateaux within the strong antiferromagnetic rung coupling regime. Gapless and gapped phases appear in turn as the magnetic fiel...

In this paper we propose and realize (the code is publicly available at https://github.com/Thrawn1985/2D-Partition-Function) an algorithm for exact calculation of partition function for planar graph models with binary spins. The complexity of the algorithm is O(N^2). Test experiments shows good agreement with Onsager's analytical solution for two-dimensional Ising model of infinite size.

We present a thorough study of the static properties of 2D models of spin-ice type on the square lattice or, in other words, the sixteen-vertex model. We use extensive Monte Carlo simulations to determine the phase diagram and critical properties of the finite dimensional system. We put forward a suitable mean-field approximation, by defining the model on carefully chosen trees. We employ the cavity (Bethe-Peierls) method to derive self-consistent equations, the fixed points ...

In the present paper the three state Potts model with competing binary interactions (with couplings $J$ and $J_p$) on the second order Bethe lattice is considered. The recurrent equations for the partition functions are derived. When $J_p=0$, by means of a construction of a special class of limiting Gibbs measures, it is shown how these equations are related with the surface energy of the Hamiltonian. This relation reduces the problem of describing the limit Gibbs measures to...

We use the cavity method to study parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single site probabilities of paths propagating along the edges of the graph. These equations are analogous to the cavity equations for equilibrium models and are exact on a tree. On graphs with exclusively directed edges we find an exact expression for the stationary distribution of the spins. We present the phase diagrams for an ...

In this thesis, we consider some spin effects in QCD and recurrence lattices with multi-site exchanges. Main topic of our manuscript are critical phenomena in spin systems defined on the recurrence lattices. Main tool of our approach is the method of recursive (hierarchical) lattices. We apply the method of dynamical mapping (or recursive lattices) for investigation of magnetic properties of the fluid and solid $^3$He, phase transitions in crystals and macromolecules. First, ...

For every physical model defined on a generic graph or factor graph, the Bethe $M$-layer construction allows building a different model for which the Bethe approximation is exact in the large $M$ limit and it coincides with the original model for $M=1$. The $1/M$ perturbative series is then expressed by a diagrammatic loop expansion in terms of so-called fat-diagrams. Our motivation is to study some important second-order phase transitions that do exist on the Bethe lattice b...

The Yang-Lee zeros of the Q-state Potts model on recursive lattices are studied for non-integer values of Q. Considering 1D lattice as a Bethe lattice with coordination number equal to two, the location of Yang-Lee zeros of 1D ferromagnetic and antiferromagnetic Potts models is completely analyzed in terms of neutral periodical points. Three different regimes for Yang-Lee zeros are found for Q>1 and 0<Q<1. An exact analytical formula for the equation of phase transition point...

Mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration-iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin-1/2 Ising model on a simple (undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction and single-ion anisotropy on...

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 the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transition appears. We discuss the connection of the six-vertex model to the conformal fie...