Related papers: Exact correlation functions of Bethe lattice spin …
The classical transverse field Ising spin- glass model with short-range interactions is investigated beyond the mean- field approximation for a real d- dimensional lattice. We use an appropriate nontrivial modification of the Bethe- Peierls…
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…
We find an exact mapping from the generalized Ising models with many-spin interactions to equivalent Boltzmann machines, i.e., the models with only two-spin interactions between physical and auxiliary binary variables accompanied by local…
We study an Ising spin system coupled to a fluctuating four-dimensional $Z_2$-Regge lattice and compare with the results of the four-dimensional Ising model on a regular lattice. Particular emphasis is placed on the phase transition of the…
We present a Green's-function theory of magnetic short-range order in the $S=1/2$ easy-plane XXZ chain based on the projection method for the dynamic spin susceptibility and a decoupling of three-spin operator products introducing vertex…
The article provides a tutorial review on how to treat Ising models within mean-field (MF), effective-field (EF) and exact methods. MF solutions of the spin-1 Blume-Capel (BC) model and the mixed-spin Ising model demonstrate a change of…
We study an integrable spin chain with an alternating array of spins S=1/2, 1 in external magnetic fields using the Bethe ansatz exact solution. The calculated magnetization possesses a cusp structure at a critical magnetic field H=H_{C},…
We consider the critical spin-spin correlation function of the 2D Ising model with a line defect which strength is an arbitrary function of position. By using path-integral techniques in the continuum description of this model in terms of…
We have developed a new method for evaluating the specific heat of lattice spin systems. It is based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the…
Motivated by recent experiments on a compound {displaying Ising-like short-range correlations on the triangular lattice, we study the anisotropic easy-axis spin-$1/2$ Heisenberg model on the triangular and kagome lattice} by performing…
We present exact integral representations of the time-dependent spin-spin correlation functions for the classical Heisenberg N-spin `squashed' equivalent neighbor model, in which one spin is coupled via the Heisenberg exchange interaction…
A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4-8)…
The finite lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the spin-1 Ising model on the square lattice. A new formalism is described that…
We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain…
The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls…
A periodic Ising model is one endowed with interactions that are invariant under translations of members of a full-rank sublattice $\mathfrak{L}$ of $\mathbb{Z}^2$. We give an exact, quantitative description of the critical temperature,…
The excited state thermodynamic Bethe ansatz (TBA) equations for the spinless Fermion model are presented by the quantum transfer matrix (QTM) approach. We introduce a more general family called T-functions and explore functional relations…
An inhomogeneous random recursive lattice was constructed from the multi-branched Husimi square lattice. The number of repeating units connected on one vertex was randomly set to be 2 or 3 with a quenched ratio $P_2$ or $P_3$ with…
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…
We consider the Ising model on the Bethe lattice with aperiodic modulation of the couplings, which has been studied numerically in Phys. Rev. E 77, 041113 (2008). Here we present a relevance-irrelevance criterion and solve the critical…