Related papers: An Ising spin - S model on generalized recursive l…
A disordered spin glass model where both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system…
We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…
We present explicit formulas for all spin matrix elements in the 2D Ising model with the nearest neighbor interaction on the finite periodic square lattice. These expressions generalize the known results [Phys. Rev. D19, (1979), 2477--2479;…
In the spirit of multi-scale modeling, we develop a theoretical framework for spin-lattice coupling that connects, on the one hand, to ab initio calculations of spin-lattice coupling parameters and, on the other hand, to the magneto-elastic…
We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin…
We study the frustration properties of the Ising model on a decorated triangular lattice with an arbitrary number of decorating spins on all lattice bonds in the framework of an exact analytical approach based on the Kramers--Wannier…
The zero-temperature random-field Ising model is solved analytically for magnetisation vs external field for a bi-layered Bethe lattice. The mechanisms of infinite avalanches which are observed for small values of disorder are established.…
The spontaneous magnetization relations for the 2D triangular and the 3D cubic lattices of the Ising model are derived by a new tractable easily calculable mathematical method. The result obtained for the triangular lattice is compared with…
The magnetic properties of the mixed spin-$\frac{1}{2}$ and spin-$\frac{7}{2}$ Ising model with a crystal-field in a longitudinal magnetic field are investigated on the Bethe lattice using exact recursion relations. The ground-state phase…
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…
We study a spin system on a large box with both Ising interaction and Sherrington-Kirpatrick couplings, in the presence of an external field. Our results are: (i) existence of the pressure in the limit of an infinite box. When both Ising…
The partition functions of ferromagnetic Ising models of square lattices in a finite magnetic field is deduced using topological considerations within a heuristic graph-theoretical approach. These equations are derived separately for low…
We consider the spherical limit of multi-matrix models on regular target graphs, for instance single or multiple Potts models, or lattices of arbitrary dimension. We show, to all orders in the low temperature expansion, that when the degree…
The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…
For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by…
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…
In a large transverse field, there is an energy cost associated with flipping spins along the axis of the field. This penalty can be employed to relate the transverse-field Ising model in a large field to the XY model in no field (when…
Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in presence of a confining magnetic field which varies with distance $|{\vec x}|$ to a "trap center", proportionally to $(|{\vec x}|/\ell)^p$, $p>0$. On a…
We address the question of geometrical as well as energetic properties of local excitations in mean field Ising spin glasses. We study analytically the Random Energy Model and numerically a dilute mean field model, first on tree-like…
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by…