Related papers: Diagonalization of replicated transfer matrices fo…
We study numerically the critical region and the disordered phase of the random transverse-field Ising chain. By using a mapping of Lieb, Schultz and Mattis to non-interacting fermions, we can obtain a numerically exact solution for rather…
In this note, we present an algorithm that yields many new methods for constructing doubly stochastic and symmetric doubly stochastic matrices for the inverse eigenvalue problem. In addition, we introduce new open problems in this area that…
Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the…
In this paper we consider a 2d random Ising system on a square lattice with nearest neighbour interactions. The disorder is short range correlated and asymmetry between the vertical and the horizontal direction is admitted. More precisely,…
Calculations in Ising model can be cumbersome and non-intuitive. Here we provide a formulation that addresses these issues for 1-D scenario. We represent the microstates of spin interactions as a diagonal matrix. This is done using two…
We study two-dimensional Ising spins, evolving through reinforcement learning using their state, action, and reward. The state of a spin is defined as whether it is in the majority or minority with its nearest neighbours. The spin updates…
In this work, exact solutions are obtained for a class of generalized gauge-invariant $n$-chain Ising models ($n=1,2,3,4$) with arbitrary multi-spin interactions that are invariant under the local $\mathbb{Z}_2$ gauge group. On a strip…
We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the…
It is demonstrated that in one-dimensional Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field, a stimulated wave of flipped spins can be triggered by a flip of a single spin. This analytically…
The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector…
We consider the renormalization of quenched bond disorder in the Ising model in the limit that it is sparse -- highly localized and vanishing in the thermodynamic limit. We begin in 1D with arbitrary disorder assigned to a finite number of…
The critical behaviour of the randomly spin-diluted Ising model in two space dimensions is investigated by a new method which combines a grand ensemble approach to disordered systems proposed by Morita with the phenomenological…
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on…
In the present article, we consider the so-called two-spin equation that describes four-level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general…
We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the…
The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…
The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the…
In this article, we study eigenvalue problems associated to self-adjoint operators and their approximation obtained by subspace projection, as used in the reduced basis method for instance. We provide error bounds between the exact…
Considering disordered electron systems we suggest a scheme that allows us to include an electron-electron interaction into a supermatrix sigma-model. The method is based on replacing the initial model of interacting electons by a fully…
We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors' correlations. It is derived by means of an exact solution to the recurrence equations for partial…