Related papers: Correspondence between spanning trees and the Isin…
The multi-branched Husimi recursive lattice has been extended to a virtual structure with fractional numbers of branches joined on one site. Although the lattice is undrawable in real space, the concept is consistent with regular Husimi…
In this paper, we investigate tree-indexed Markov chains (Gibbs measures) defined by a Hamiltonian that couples two Ising layers: hidden spins \(s(x) \in \{\pm 1\}\) and observed spins \(\sigma(x) \in \{\pm 1\}\) on a Cayley tree. The…
We study analytically the Ising model coupled to random lattices in dimension three and higher. The family of random lattices we use is generated by the large N limit of a colored tensor model generalizing the two-matrix model for Ising…
We study magnetic properties of the $S=1/2$ Ising-like XXZ model on the Shastry-Sutherland lattices with long-range interactions, using the quantum Monte Carlo method. This model shows magnetization plateau phases at one-half and one-third…
Thermodynamic properties of the ferromagnetic Ising model on the hierarchical pentagon lattice is studied by means of the tensor network methods. The lattice consists of pentagons, where 3 or 4 of them meet at each vertex. Correlation…
It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with…
We study the two-dimensional square lattice Ising ferromagnet and antiferromagnet with a magnetic field by using tensor network method. Focusing on the role of guage fixing, we present the partition function in terms of a tensor network.…
Fractals are ubiquitous in the natural world, and their connection with phase transitions has been widely observed. This study investigates mechanisms of fractal formation from the perspective of phase transitions. A novel set of…
The magnetic and entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on a triangulated Kagome lattice are analyzed by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. Because…
Let $G$ be the product of finitely many trees $T_1\times T_2 \times \cdots \times T_N$, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that…
In this paper, we develop a new method to produce explicit formulas for the number $\tau(n)$ of spanning trees in the undirected circulant graphs $C_{n}(s_1,s_2,\ldots,s_k)$ and $C_{2n}(s_1,s_2,\ldots,s_k,n).$ Also, we prove that in both…
We consider long strips of finite width $L \leq 13$ sites of ferromagnetic Ising spins with random couplings distributed according to the binary distribution: $P(J_{ij})= {1 \over 2} ( \delta (J_{ij} -J_0) + \delta (J_{ij} -rJ_0) ) ,\ 0 < r…
The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a softly BRST-broken version of QCD and possesses a quark mass function…
In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local…
We study the statistical properties of the sum $S_t=\int_{0}^{t}dt' \sigma_{t'}$, that is the difference of time spent positive or negative by the spin $\sigma_{t}$, located at a given site of a $D$-dimensional Ising model evolving under…
A streamlined derivation of the Kac-Ward formula for the planar Ising model's partition function is presented and applied in relating the kernel of the Kac-Ward matrices' inverse with the correlation functions of the Ising model's…
We consider the thermodynamic properties of the quasi-two-dimensional spin-half Heisenberg ferromagnet on the stacked square and the stacked kagom\'e lattices by using the spin-rotation-invariant Green's function method. We calculate the…
We study the ferromagnetic Ising model on the infinite $d$-regular tree under the free boundary condition. This model is known to be a factor of IID in the uniqueness regime, when the inverse temperature $\beta\ge 0$ satisfies $\tanh \beta…
The Ising model on an alternating triangular lattice with the nearest-neighbor interaction in a magnetic field is presented. Exact solution of this model is found. The thermodynamic quantities, like free energy, specific heat a finite…
A numerical study of finite temperature features of thermodynamical observables is performed for the lattice 2d Ising model. Our results support the conjecture that the Finite Size Scaling analysis employed in the study of integrable…