Random Magnetic Field Research Articles

Microcanonical Analysis of the Random Energy Model in a Random Magnetic Field

We study the spin glass system consisting of a Random Energy Model coupled with a random magnetic field. This system was investigated by de Oliveira Filho, da Costa and Yokoi (Phys. Rev. E 74 [2006]) who computed the free energy. In this paper, we recover their result rigorously using elementary large deviations arguments and a conditional second moment method. Our analysis extends at the level of fluctuations of the ground states. In particular, we prove that the joint distribution of the extremal energies has the law of a Poisson process with exponential density after a recentering, which is random as opposed to the standard REM. One consequence is that the Gibbs measure of the model exhibits a one-step replica symmetry breaking as argued by de Oliveira Filho et al. using the replica method.

Supersymmetry approach to delocalization transitions in a network model of the weak-field quantum Hall effect and related models

We consider a recently proposed network model of the integer quantum Hall (IQH) effect in a weak magnetic field. Using a supersymmetry approach, we reformulate the network model in terms of a superspin ladder. A subsequent analysis of the superspin ladder and the corresponding supersymmetric nonlinear sigma model allows us to establish the phase diagram of the network model, and the form of the critical line of the weak-field IQH transition. Our results confirm the universality of the IQH transition, which is described by the same sigma model in strong and weak magnetic fields. We apply the suspersymmetry method to several related network models that were introduced in the literature to describe the quantum Hall effect in graphene, the spin-degenerate Landau levels, and localization of electrons in a random magnetic field.

Decay of the rotary echoes for the spin of a nitrogen-vacancy center in diamond

We study dynamics of the electron spin of a nitrogen-vacancy (NV) center subjected to a strong driving field with periodically reversed direction (train of rotary echoes). We use analytical and numerical tools to analyze in detail the form and timescales of decay of the rotary echo train, modeling the decohering spin environment as a random magnetic field. We demonstrate that the problem can be exactly mapped onto a model of spin 1 coupled to a single bosonic mode with imaginary frequency. This mapping allows comprehensive analytical investigation beyond the standard Bloch-Redfield-type approaches. We explore the decay of the rotary echo train under assumption of strong driving, and identify the most important regimes of the decay. The analytical results are compared with the direct numerical simulations to confirm quantitative accuracy of our study. We present the results for realistic environment of substitutional nitrogen atoms (P1 centers), and provide a simplified but accurate description for decay of the rotary echo train of the NV center's spin. The approach presented here can also be used to study decoherence and longitudinal relaxation of other spin systems under conditions of strong driving.

Proposal for direct measurement of random fields in theLiHoxY1−xF4crystal

The random field Ising model (RFIM) is central to the study of disordered systems. Yet, for a long time it eluded realization in ferromagnetic systems because of the difficulty to produce locally random magnetic fields. Recently it was shown that in anisotropic dipolar magnetic insulators, the archetypal of which is the $LiHo_xY_{1-x}F_4$ system, the RFIM can be realized in both ferromagnetic and spin glass phases. The interplay between an applied transverse field and the offdiagonal terms of the dipolar interaction produce effective longitudinal fields, which are random in sign and magnitude as a result of spatial dilution. In this paper we use exact numerical diagonalization of the full Hamiltonian of Ho pairs in $LiHo_xY_{1-x}F_4$ to calculate the effective longitudinal field beyond the perturbative regime. In particular, we find that nearby spins can experience an effective field larger than the intrinsic dipolar broadening (of quantum states in zero field) which can therefore be evidenced in experiments. We then calculate the magnetization and susceptibility under several experimental protocols, and show how these protocols can produce direct measurement of the effective longitudinal field.

Reversible Disorder in a Room Temperature Ferromagnet

Random magnetic fields, varying from site to site in a magnetic material, are a form of disorder that can determine the local architecture and stability of the magnetic state. In a ferromagnet, the application of an external magnetic field can amplify the effects of the internal random fields and, in principle, harden a magnetic domain, without changing temperature and only for as long as the external field is present. Here, the rare-earth compound Nd 2Fe14B, formed with a granular morphology of random-packed, elongated grains, is an experimental realization of the Random Field Ising Model in a room temperature ferromagnet. The application of magnetic fields transverse to the easy axis tunes the coupling between the structural disorder and the magnetic pinning properties. This material both illuminates the intricacies of tunable disorder and serves as a guidepost along the way to developing increased-density magnetic storage media. Application of a transverse magnetic field can reversibly tune the magnetic hardness of a disordered uniaxial, high anisotropy rare earth magnet at room temperature. Random field effects control the effective strength of the material's intrinsic disorder, providing a convenient control knob for rapidly and isothermally switching between different computationally relevant magnetic characteristics. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

JITTER POLARIZATION FOR GRB PROMPT EMISSION

The radiation of relativistic electrons in random and small-scale magnetic field is called jitter radiation. We apply jitter process to study the polarization feature of GRB prompt emission. A two-dimensional compressed slab which contains stochastic magnetic field is applied in our model. If jitter condition is satisfied, the high degree polarization can be achieved when the angle between line-of-sight and slab plane is small. Moreover, micro-emitters with mini-jet structure and jet off-axis effect are considered.

The Sherrington–Kirkpatrick spin glass model in the presence of a random field with a joint Gaussian probability density function for the exchange interactions and random fields

The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The Sherrington–Kirkpatrick Ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method. The two random variables (exchange integral interaction and random magnetic field) are drawn from a joint Gaussian probability density function characterized by a correlation coefficient ρ. The thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density. The de Almeida–Thouless line is explored as a function of temperature, ρ and other system parameters. The entropy for zero temperature as well as for non zero temperatures is partly negative or positive, acquiring positive branches as h0 increases.

Absolutely calibrated radio polarimetry of the inner Galaxy at 2.3 and 4.8 GHz

We present high sensitivity and absolutely calibrated images of diffuse radio polarisation at a resolution of about 10 arcmin covering the range 10 degr <l<34 degr and |b|<5 degr at 2.3 GHz from the S-band Parkes All Sky Survey and at 4.8 GHz from the Sino-German 6 cm polarisation survey of the Galactic plane. Strong depolarisation near the Galactic plane is seen at 2.3 GHz, which correlates with strong Halpha emission. We ascribe the depolarisation to spatial Faraday rotation measure fluctuations of about 65 rad/m2 on scales smaller than 6-9 pc. We argue that most (about 90%) of the polarised emission seen at 4.8 GHz originates from a distance of 3-4 kpc in the Scutum arm and that the random magnetic field dominates the regular field there. A branch extending from the North Polar Spur towards lower latitudes can be identified from the polarisation image at 4.8 GHz but only partly from the polarised image at 2.3 GHz, implying the branch is at a distance larger than 2-3 kpc. We show that comparison of structure functions of complex polarised intensity with those of polarised intensity can indicate whether the observed polarised structures are intrinsic or caused by Faraday screens. The probability distribution function of gradients from the polarisation images at 2.3 GHz indicates the turbulence in the warm ionised medium is transonic.

An observational test for correlations between cosmic rays and magnetic fields

We derive the magnitude of fluctuations in total synchrotron intensity in the Milky Way and M33, from both observations and theory under various assumption about the relation between cosmic rays and interstellar magnetic fields. Given the relative magnitude of the fluctuations in the Galactic magnetic field (the ratio of the rms fluctuations to the mean magnetic field strength) suggested by Faraday rotation and synchrotron polarization, the observations are inconsistent with local energy equipartition between cosmic rays and magnetic fields. Our analysis of relative synchrotron intensity fluctuations indicates that the distribution of cosmic rays is nearly uniform at the scales of the order of and exceeding $100\p$, in contrast to strong fluctuations in the interstellar magnetic field at those scales. A conservative upper limit on the ratio of the the fluctuation magnitude in the cosmic ray number density to its mean value is 0.2--0.4 at scales of order 100\,pc. Our results are consistent with a mild anticorrelation between cosmic-ray and magnetic energy densities at these scales, in both the Milky Way and M33. Energy equipartition between cosmic rays and magnetic fields may still hold, but at scales exceeding 1\,kpc. Therefore, we suggest that equipartition estimates be applied to the observed synchrotron intensity smoothed to a linear scale of kiloparsec order (in spiral galaxies) to obtain the cosmic ray distribution and a large-scale magnetic field. Then the resulting cosmic ray distribution can be used to derive the fluctuating magnetic field strength from the data at the original resolution. The resulting random magnetic field is likely to be significantly stronger than existing estimates.

Effects of the trimodal random field on the magnetic properties of a spin-1 Ising nanotube

In this work, the hysteresis behavior of a nanotube, consisting of a ferromagnetic core of spin-1 atoms surrounded by a ferromagnetic shell of spin-1 atoms with ferro- or anti-ferromagnetic interfacial coupling is studied in the presence of a random magnetic field. Based on a probability distribution method, the effective-field theory has been used to investigate the effects of the random magnetic field, the interfacial coupling constant, and the temperature on the hysteresis loops of the nanotube. Some characteristic behaviors have been found, such as the existence of double or triple hysteresis loops for appropriate values of the system parameters. The remanent magnetization and the coercive field, as functions of the temperature, are examined.

Studying Galactic interstellar turbulence through fluctuations in synchrotron emission

The characteristic outer scale of turbulence and the ratio of the random to ordered components of the magnetic field are key parameters to characterise magnetic turbulence in the interstellar gas, which affects the propagation of cosmic rays within the Galaxy. We provide new constraints to those two parameters. We use the LOw Frequency ARray (LOFAR) to image the diffuse continuum emission in the Fan region at (l,b) (137.0,+7.0) at 80"x70" resolution in the range [146,174] MHz. We detect multi-scale fluctuations in the Galactic synchrotron emission and compute their power spectrum. Applying theoretical estimates and derivations from the literature for the first time, we derive the outer scale of turbulence and the ratio of random to ordered magnetic field from the characteristics of these fluctuations . We obtain the deepest image of the Fan region to date and find diffuse continuum emission within the primary beam. The power spectrum of the foreground synchrotron fluctuations displays a power law behaviour for scales between 100 and 8 arcmin with a slope of (-1.84+/-0.19). We find an upper limit of about 20 pc for the outer scale of the magnetic interstellar turbulence toward the Fan region. We also find a variation of the ratio of random to ordered field as a function of Galactic coordinates, supporting different turbulent regimes. We use power spectra fluctuations from LOFAR as well as earlier GMRT and WSRT observations to constrain the outer scale of turbulence of the Galactic synchrotron foreground, finding a range of plausible values of 10-20 pc. Then, we use this information to deduce lower limits of the ratio of ordered to random magnetic field strength. These are found to be 0.3, 0.3, and 0.5 for the LOFAR, WSRT and GMRT fields considered respectively. Both these constraints are in agreement with previous estimates.

Organic magnetoresistance under resonant ac drive

We study the spin dynamics of an electron-hole pair in a random hyperfine magnetic field and an external field, B0, under a resonant drive with frequency omega0 = gamma B0. The fact that the pair decays by recombination exclusively from a singlet configuration, S, in which the spins of the pair-partners are entangled, makes this dynamics highly nontivial. Namely, as the amplitude, B1, of the driving field grows, mixing all of the triplet components, the long-living modes do not disappear, but evolve from T+, T- into (T+ +/- sqrt(2) T0 + T-)/2. Upon further increase of B1, the lifetime of the S-mode is cut in half, while the T0-mode transforms into an antisymmetric combination (T- - T-)/sqrt(2) and acquires a long lifetime, in full analogy to the superradiant and subradiant modes in the Dicke effect. Peculiar spin dynamics translates into a peculiar dependence on B1. In particular, at small B1, the radiation-induced correction to the current is linear in B1.

APPLICATION OF JITTER RADIATION: GAMMA-RAY BURST PROMPT POLARIZATION

A high-degree of polarization of gamma-ray burst (GRB) prompt emission has been confirmed in recent years. In this paper, we apply jitter radiation to study the polarization feature of GRB prompt emission. In our framework, relativistic electrons are accelerated by turbulent acceleration. Random and small-scale magnetic fields are generated by turbulence. We further determine that the polarization property of GRB prompt emission is governed by the configuration of the random and small-scale magnetic fields. A two-dimensional compressed slab, which contains stochastic magnetic fields, is applied in our model. If the jitter condition is satisfied, the electron deflection angle in the magnetic field is very small and the electron trajectory can be treated as a straight line. A high-degree of polarization can be achieved when the angle between the line of sight and the slab plane is small. Moreover, micro-emitters with mini-jet structure are considered to be within a bulk GRB jet. The jet "off-axis" effect is intensely sensitive to the observed polarization degree. We discuss the depolarization effect on GRB prompt emission and afterglow. We also speculate that the rapid variability of GRB prompt polarization may be correlated with the stochastic variability of the turbulent dynamo or the magnetic reconnection of plasmas.

Topology Trivialization and Large Deviations for the Minimum in the Simplest Random Optimization

Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)- dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust region subproblem" or "constraint least square problem". When both terms in the cost function are random this amounts to studying the ground state energy of the simplest spherical spin glass in a random magnetic field. We first identify and study two distinct large-N scaling regimes in which the linear term (magnetic field) leads to a gradual topology trivialization, i.e. reduction in the total number N_{tot} of critical (stationary) points in the cost function landscape. In the first regime N_{tot} remains of the order $N$ and the cost function (energy) has generically two almost degenerate minima with the Tracy-Widom (TW) statistics. In the second regime the number of critical points is of the order of unity with a finite probability for a single minimum. In that case the mean total number of extrema (minima and maxima) of the cost function is given by the Laplace transform of the TW density, and the distribution of the global minimum energy is expected to take a universal scaling form generalizing the TW law. Though the full form of that distribution is not yet known to us, one of its far tails can be inferred from the large deviation theory for the global minimum. In the rest of the paper we show how to use the replica method to obtain the probability density of the minimum energy in the large-deviation approximation by finding both the rate function and the leading pre-exponential factor.

Brain tissue classification based on DTI using an improved Fuzzy C-means algorithm with spatial constraints

We present an effective method for brain tissue classification based on diffusion tensor imaging (DTI) data. The method accounts for two main DTI segmentation obstacles: random noise and magnetic field inhomogeneities. In the proposed method, DTI parametric maps were used to resolve intensity inhomogeneities of brain tissue segmentation because they could provide complementary information for tissues and define accurate tissue maps. An improved fuzzy c-means with spatial constraints proposal was used to enhance the noise and artifact robustness of DTI segmentation. Fuzzy c-means clustering with spatial constraints (FCM_S) could effectively segment images corrupted by noise, outliers, and other imaging artifacts. Its effectiveness contributes not only to the introduction of fuzziness for belongingness of each pixel but also to the exploitation of spatial contextual information. We proposed an improved FCM_S applied on DTI parametric maps, which explores the mean and covariance of the feature spatial information for automated segmentation of DTI. The experiments on synthetic images and real-world datasets showed that our proposed algorithms, especially with new spatial constraints, were more effective.

Spin-1 Blume—Capel model with longitudinal random crystal and transverse magnetic fields: A mean-field approach

The spin-1 Blume—Capel model with transverse Ω and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 — p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ = Ω/J and p at zero h. Thus, the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.

Stability of magnetic fields in non-barotropic stars: an analytic treatment

Magnetic fields in upper main-sequence stars, white dwarfs, and neutron stars are known to persist for timescales comparable to their lifetimes. From a theoretical perspective this is problematic, as it can be shown that simple magnetic field configurations are always unstable. In non-barotropic stars, stable stratification allows for a much wider range of magnetic field structures than in barotropic stars, and helps stabilize them by making it harder to induce radial displacements. Recent simulations by Braithwaite and collaborators have shown that, in stably stratified stars, random initial magnetic fields evolve into nearly axisymmetric configurations with both poloidal and toroidal components, which then remain stable for some time. It is desirable to provide an analytic study of the stability of such fields. We write an explicit expression for a plausible equilibrium structure of an axially symmetric magnetic field with both poloidal and toroidal components of adjustable strengths, in a non-barotropic static fluid star, and study its stability using the energy principle. We construct a displacement field that should be a reasonable approximation to the most unstable mode of a toroidal field, and confirm Braithwaite's result that a given toroidal field can be stabilized by a poloidal field containing much less energy than the former. This is consistent with the speculation that the toroidal field is the main reservoir powering magnetar activity. The deformation of a neutron star caused by the hidden toroidal field can also cause emission of gravitational waves.

Random field effects on the anisotropic quantum Heisenberg model with Gaussian random magnetic field distribution

The effect of a zero-centered Gaussian random magnetic field distribution on the phase transition properties of the anisotropic quantum Heisenberg model has been investigated on a honeycomb lattice within the framework of effective field theory (EFT) for a two-spin cluster (which is abbreviated as EFT-2). Particular attention has been devoted to investigation of the effect of the anisotropy in the exchange interaction on a system with Gaussian random magnetic field distribution. The variation of the critical temperature with the randomness parameter (i.e., the width of the distribution) has been obtained for several anisotropy parameters. Critical Gaussian distribution width values, which make the critical temperature zero, have been obtained. Moreover, it has been concluded that all critical temperatures are of second order, and that reentrant behavior does not exist in the phase diagrams.

Quantum Zeno and anti-Zeno effects measured by transition probabilities

Using numerical calculations, we compare the collective transition probabilities of many spins in random magnetic fields, subject to either frequent projective measurements, frequent phase modulations, or a mix of modulations and measurements. For three different distribution functions (Gaussian, Lorentzian, and exponential) we consider here, the transition probability under frequent modulations is suppressed most if the pulse delay is short and the evolution time is larger than a critical value. Furthermore, decoherence freezing (with a transition rate equals to zero) occurs when there are frequent phase modulations, while the transition rate only decreases when there are frequent measurements and a mix of them, as the pulse delay approaches zero. In the large pulse-delay region, however, the transition probabilities under frequent modulations are enhanced more than those under either frequent measurements or a mix of modulations and measurements.

Spin-glass freezing in Kondo-lattice compounds in the presence of a random and a transverse magnetic field

The present work studies the effects of a random magnetic field on the competition among Kondo effect, spin glass (SG) phase and ferromagnetic (FE) order in disordered cerium systems such as CeNi1−xCux. A Kondo lattice model is used with an intersite disordered interaction Jij between localized Ising spins in the presence of a transverse magnetic field Γ and a longitudinal random magnetic field. The disorders introduced by Jij and the random field follow Gaussian distributions. They are treated within the one-step replica symmetry breaking procedure. The results suggest that the presence of a random field affects strongly the FE and SG phases. It can disrupt the FE order completely and reduces the SG phase region. It can also introduce an independent spin phase that can coexist within the Kondo regime at high Kondo interaction Jk. On the other hand, the Γ field introduces quantum spin fluctuations able to destroy the magnetic order by decreasing the critical temperature towards a quantum critical point. In addition, the Kondo states can only occur at higher Jk values as Γ increases.