Ground states and thermal states of the random field Ising model

The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random field and external field strength. Thermal states and thermodynamic properties are obtained for all temperatures using the Wang-Landau algorithm. The specific heat and susceptibility typically display sharp peaks in the critical region for large systems and strong disorder. These sharp peaks result from large domains flipping. For a given realization of disorder, ground states and thermal states near the critical line are found to be strongly correlated--a concrete manifestation of the zero temperature fixed point scenario.     

Random infinite-volume Gibbs states for the Curie-Weiss random field Ising model

An approach to the definition of infinite-volume Gibbs states for the (quenched) random-field Ising model is considered in the case of a Curie-Weiss ferromagnet. It turns out that these states are random quasi-free measures. They are random convex linear combinations of the free product-measures shifted by the corresponding effective mean fields. The conditional self-averaging property of the magnetization related to this randomness is also discussed.This paper is dedicated to Robert A. Minlos on the occasion of his 60th birthday.     

Analytical verification of scaling laws for the Ising model with external field in fractal lattices

We use an exact recursion procedure to verify analytically, without any intermediary numerical calculation, the validity of the hyperscaling (Josephson) law extended to fractals, the Rushbrooke and Griffiths scaling laws for the Ising ferromagnet with external magnetic field in the whole family of Migdal-Kadanoff-like hierarchical lattices.     

Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

We investigate the zero-temperature quantum phase transition of the randombond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter and correlation function probability distribution show a nontrivial scaling near the critical point, which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.     

The Ising model in a random magnetic field

The existence of a spontaneous magnetization in the three-dimensional Ising model in a weak random magnetic field (RFIM) is investgated. Following Imry and Ma, we consider the energy change, E, from the fully aligned ferromagnetic state caused by flipping all the spins inside a connected surface, . It is proved rigorously that with high probability, E is positive forall enclosing the origin. Under the unproven assumption that the expectation value of the spin at one site is weakly correlated with the random fields at far away sites (which is true if surfaces within surfaces can be ignored) it follows that the three-dimensional RFIM has a spontaneous magnetization at low temperatures. The proof works for all dimensions greater than two, providing support for the conjecture that two is the lower critical dimension.Work supported in part by NSF grant No. DMR 8100417.     

Ground states versus low-temperature equilibria in random field Ising chains

Random walk arguments and exact numerical computations are used to study one-dimensional random field chains. The ground state structure is described with absorbing and non-absorbing random walk excursions. At low temperatures, the local magnetization follows the ground state except at regions where a local random field fluctuation makes thermal excitations easier. This is explained by the random walk picture, implying that the magnetization lengthscale is a product of the domain size and the thermal excitation scale. Received 16 October 2000 and Received in final form 7 June 2001     

Density of states for nearly-free electrons in a uniform magnetic field

The density of states of an electron gas in the presence of a uniform magnetic field and a weak periodic lattice-potential is calculated in the second Born-approximation.     

Random field Ising model and community structure in complex networks

We propose a method to determine the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field B_s = +∞, B_t = -∞, and B_i≠s,t=0 for a node pair s and t. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of s and t. Our method provides a criterion for the existence of the community structure, and is applicable equally well to unweighted and weighted networks. We demonstrate the performance of the method by applying it to the Barabási-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network. (Ising, Potts, etc.)     

Thermodynamic geometry of a kagome Ising model in a magnetic field

We derived the thermodynamic curvature of the Ising model on a kagome lattice under the presence of an external magnetic field. The curvature was found to have a singularity at the critical point. We focused on the zero field case to derive thermodynamic curvature and its components near the criticality. According to standard scaling, scalar curvature R   behaves as |β−_βc|^α−2${|\beta -{\beta }_c|}^{\alpha -2}$ for α>0$\alpha >0$ where β is the inverse temperature and α is the critical exponent of specific heat. In the model considered here in which α is zero, we found that R   behaves as |β−_βc|^α−1${|\beta -{\beta }_c|}^{\alpha -1}$.     

The density of states for carbon nanotubes in a uniform magnetic field

Dispersion laws for carbon nanotubes in a uniform magnetic field are obtained in an explicit form in a zero-range-potential model. The band structure of the spectrum is studied, and the density of states is calculated numerically.     

Donor-bound electron states in a two-dimensional quantum ring under uniform magnetic field

The electron states in a two-dimensional GaAs/AlGaAs quantum ring are theoretically studied in effective mass approximation. On-centre donor impurity and uniform magnetic field perpendicular to the ring plane are taken into account. The energy spectrum with different angular momentum changes dramatically with the geometry of the ring. The donor impurity reduces the energies with an almost fixed value; however, the magnetic field alters energies in a more complex way. For example, energy levels under magnetic field will cross each other when increasing the inner radius and outer radius of the ring, leading to the fact that the arrangement of energy levels is distinct in certain geometry of the ring. Moreover, energy levels with negative angular momentum exhibit the non-monotonous dependence on the increasing magnetic field.     

Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory

Recently,Shi et al.[2008 Phys.Lett.A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory(EFT) and a mean-field theory(MFT).The MFT results are in conflict with those of the earlier work of Tom’e and de Oliveira,[1990 Phys.Rev.A 41 4251].We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tom’e and de Oliveira;hence the dynamic phase diagrams calculated by Shi et al.are incomplete within both theories,except the low values of frequencies for the MFT calculation.We also investigate the influence of external field frequency(ω) and static external field amplitude(h0) for both MFT and EFT calculations.We find that the behaviour of the system strongly depends on the values of ω and h0.     

Phase diagram of spin-S Ising model in a random magnetic field

A spin-S Ising model with a random magnetic field is studied in the mean field approximation. It is shown that there is no long-range-order, for any value of S, for the value of the fields $\text{h}\text{SJz}\text{? 0.5}$. Complete phase diagrams are constructed numerically for $\text{S = 1}\text{and}\text{S =}\text{3}\text{2}$.     

Ground state of an antiferromagnet with uniform antisymmetric exchange in a magnetic field

A system of two nonlinear differential equations for sublattice angles is proposed to describe the spin orientation distribution in a planar antiferromagnet with uniform antisymmetric exchange in a magnetic field. This system involves the initial symmetry of the problem and is reduced to a single delay differential equation. The solutions of this system are parameterized by the initial condition imposed on the angle of one sublattice at the hyperbolic singular point of the phase space. The numerical analysis of the stability boundary of soliton solutions demonstrates that the transition to the commensurate phase takes place outside the region where the stochastic solutions appear and is accompanied by the magnetization jump Δm ∼ 10⁻¹ m.     

The Aharonov-Bohm effect for nonstationary quasiclassical trajectory-coherent states in a uniform magnetic field

Approximate (as h 0) dynamic states in the form of nondiffusing wave packets, localized in the vicinity of a classical trajectory (nonintersecting the solenoid), quasiclassical nonstationary trajectory-coherent states, are constructed for nonrelativistic electron motion in a uniform magnetic field in the presence of an infinitely thin and long solenoid. The occurrence of the Aharonov-Bohm effect in such states is investigated. Special cases of electron motion — in a uniform magnetic field and in the solenoid field — are considered.Moscow Institute of Electronic Machinery. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 83–90, October, 1992.     

一维倾斜场伊辛模型中的纠缠特性

在一维倾斜场伊辛模型中, 利用并发度和Q测量函数分别对系统的两体纠缠和整体纠缠进行度量, 通过讨论系统中量子纠缠的动力学特性, 能够体现出系统的可积和不可积行为. 由系统基态的纠缠特性可以发现只要倾角不为零时, 系统的Q测量函数会随着磁场的增大而减少, 而用并发度刻画的系统的相变特性, 随着磁场倾角的增大发生了变化. 考虑系统的动力学行为发现, 在一维倾斜场伊辛模型中, 不可积性会抑制两体纠缠, 却促进系统整体纠缠生成. 关键词： 伊辛模型 不可积性 两体纠缠 整体纠缠