Related papers: Relevant Analytic Spontaneous Magnetization Relati…
We present a systematic small-correlation expansion to solve the inverse Ising problem: find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in…
Two-component mixtures in optical lattices reveal a rich variety of different phases. We employ an exact diagonalization method to obtain the relevant correlation functions in hexagonal optical lattices to characterize those phases. We…
Recently, machine-learning methods have been shown to be successful in identifying and classifying different phases of the square-lattice Ising model. We study the performance and limits of classification and regression models. In…
Kinetic Ising models on the square lattice with both nearest-neighbor interactions and self-interaction are studied for the cases of random sequential updating and parallel updating. The equilibrium phase diagrams and critical dynamics are…
Plateaux in the magnetization curves of the square, triangular and hexagonal lattice spin-1/2 XXZ antiferromagnet are investigated. One finds a zero magnetization plateau (corresponding to a spin-gap) on the square and hexagonal lattice…
Form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary disposition of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions ($N$) is…
Finite-range interacting spin models are the simplest models to study the effect of beyond nearest-neighbour interactions and access new effects caused by the range of the interactions. Recent experiments have reached the regime of dominant…
Spontaneous magnetization and magnetic susceptibility originated from the pseudovector-type four-point interaction between quarks are calculated in quark matter with zero temperature and finite quark chemical potential by using the…
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 report the conjectures on the three-dimensional (3D) Ising model on simple orthorhombic lattices, together with the details of calculations for a putative exact solution. Two conjectures, an additional rotation in the fourth curled-up…
Magnetization plateaus and phase diagrams of the extended Ising model on the Shastry-Sutherland lattice with the first $(J_1)$, second $(J_2)$, third $(J_3)$ fourth $(J_4)$ and fifth $(J_5)$ nearest-neighbour spin couplings are studied by…
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous proof for the behavior of the 2D Ising lattice gas, at a finite volume and a fixed excess \delta M of particles (spins) above the ambient gas density (spontaneous…
The spin system of the $2d$ Ising model having a hexagonal-lattice is simulated using non-deterministic Cellular Automata. The method to implement this program is outlined and our results show a good approximation to the exact analytic…
The existence of spontaneous magnetization of Ising spins on directed Barabasi-Albert networks is investigated with seven neighbors, by using Monte Carlo simulations. In large systems we see the magnetization for different temperatures T to…
We show that by displacing two optical lattices with respect to each other, we may produce interactions similar to the ones describing ferro-magnetism in condensed matter physics. We also show that particularly simple choices of the…
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)…
In 2011 I reviewed the calculation by Onsager and Kaufman of the spontaneous magnetization of the square-lattice Ising model, which Onsager announced in 1949 but never published. I have recently been alerted to further original papers that…
Despite their simple formulation, short range classical antiferromagnetic Ising models on frustrated lattices give rise to exotic phases of matter, in particular due to their macroscopic ground state degeneracy. Recent experiments on…
We present a simple, but efficient, way to calculate connection matrices between sets of independent local solutions, defined at two neighboring singular points, of Fuchsian differential equations of quite large orders, such as those found…
Using Monte Carlo techniques, the critical behaviour at edges and corners of the three-dimensional Ising model is studied. In particular, the critical exponent $\beta_2$ of the local magnetization at edges formed by two intersecting free…