Related papers: Small-Network Approximations for Geometrically Fru…
In this paper, we performed the comprehensive studies of frustration properties in the Ising model on a decorated square lattice in the framework of an exact analytical approach based on the Kramers--Wannier transfer matrix method. The…
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…
Frustration in the presence of competing interactions is ubiquitous in the physical sciences and is a source of degeneracy and disorder, giving rise to new and interesting physical phenomena. Perhaps nowhere does it occur more simply than…
The antiferromagnetic Ising model in small-world networks generated from two-dimensional regular lattices has been studied. The disorder introduced by long-range connections causes frustration, which gives rise to a spin-glass phase at low…
The spatial photonic Ising machine (SPIM) [D. Pierangeli et al., Phys. Rev. Lett. 122, 213902 (2019)] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems…
The minimal training set to train a working CNN is explored in detail. The considered model is the frustrated $J_1$-$J_2$ Ising model on the square lattice. Here $J_1 < 0$ and $J_2 > 0$ are the nearest and next-to-nearest neighboring…
The extended model of two-leg Ising spin ladder with trimer rungs and next nearest neighbor interaction (NNN) in an external magnetic field is studied using the transfer matrix and linear renormalization group methods. In the standard…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
The antiferromagnetic Ising model on a triangular lattice (AFIT) exemplifies the most classical frustration system, arising from its triangular geometry that prevents all interactions from being simultaneously satisfied. Understanding…
Magnetism plays a key role in modern technology as essential building block of many devices used in daily life. Rich future prospects connected to spintronics, next generation storage devices or superconductivity make it a highly dynamical…
A frustrated Ising model on a diamond hierarchical lattice is studied. We obtain the exact partition function of this model and calculate the transition temperature, specific heat, entropy, magnetization, and ferromagnetic correlation…
This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the…
We propose a general method for studying systems that display excitations with arbitrarily low energy in their low-temperature phase. We argue that in a rectangular right prism geometry, with longitudinal size much larger than the…
We develop a technique for calculating three-dimensional classical partition functions using projected entangled-pair states (PEPS). Our method is based on variational PEPS optimization algorithms for two-dimensional quantum spin systems,…
In this study, critical behavior of low dimensional magnetic systems as cyano-bridged Tb(III)-Cr(III) bimetallic assembly was investigated with the mixed spin $3$- spin $3/2$ Ising model. The mixed spin Ising model is simulated with…
A non-equilibrium open-dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial…
We study the two-dimensional Ising model on a network with a novel type of quenched topological (connectivity) disorder. We construct random lattices of constant coordination number and perform large scale Monte Carlo simulations in order…
The statistics of critical spin-spin correlation functions in Ising systems with non-frustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and…