Presence Of Random Field Research Articles

Coercivity induced by random field at ferromagnetic and antiferromagnetic interfaces

In the presence of random fields at an interface between a ferromagnetic and an antiferromagnetic layer, the domain walls in the ferromagnetic layer are pinned by local minimum energy. To move the domain walls, an applied magnetic field must be large enough to overcome statistically fluctuating energy. We have calculated this energy and found that the coercivity can be as large as a few kOe for a thin ferromagnetic layer. It is also found that the coercive field at low temperature scales as 1/ t 3/2 where t is the F layer thickness, and the coercive field decreases strongly with temperature.

Quantum rotors in the presence of a random field

We have studied the $M$-component quantum rotor Hamiltonian in the presence of a static random field (uncorrelated and Gaussian distributed) on each site of the lattice. This model is essentially an $M$-component generalization of the transverse Ising model in a random longitudinal field. We find that even the zero-temperature transition in the model from a ferromagnetic to the paramagnetic phase, is dominated by the random-field fixed point, which essentially determines the finite-temperature transition in the above model and the transition in the classical $M$-vector model in the presence of a random field. With the assumption that the transition is of continuous nature, we employ a standard renormalization-group method to study the effective classical action of the model and extract the exponents associated with the transition. We do also extend these renormalization-group calculations to the spherical $(\stackrel{\ensuremath{\rightarrow}}{M}\ensuremath{\infty})$ limit. Finally, we develop a scaling argument that describes the zero-temperature transition and clearly indicates the occurrence of the dynamical exponents in the different scaling relations. We also qualitatively discuss the dynamic scaling scenario in the quantum model.

Domain size in the presence of random fields

Domain size in the presence of random fields

Quantum site-random XY spin glasses in a random field

A quantum spherical version of the site-random XY model in the presence of random field is presented in the boson space. In the phase diagram drawn as a function of the strength of random field, we find that the ferromagnetic and spin-glass phases are reduced by quantum fluctuations and destroyed completely by random-field fluctuations with sufficiently large values of the random-field variance.

Mean-field calculations for the axial next-nearest-neighbor Ising model in a random field

We consider a mean-field version of an Ising model on a simple cubic lattice with competing interactions between nearest and next-nearest neighbors along the $z$ axis in the presence of a random field. We obtain phase diagrams in terms of the temperature, the ratio of the strengths of the competing interactions, and the intensity of the $\ifmmode\pm\else\textpm\fi{}H$ random fields. There are no drastic qualitative changes for weak random fields. The effect of moderate random fields consists in the change of order of the transitions to the disordered phase. Although the transition from the paramagnetic to the ordered (ferromagnetic and modulated) phases in the absence of a random field is always continuous, for random fields of moderate intensity we show the appearance of tricritical points separating the critical lines (at higher temperatures) from a line of first-order transitions (at lower temperatures). We show the presence of modulated phases with disordered layers (with zero magnetization) and the pinching of the corresponding regions in the phase diagram. The modulated structures are destroyed in the presence of strong random fields.

Proton pseudoglass-to-fast-ion-conductor phase transition inCsHSO4

The temperature dependences of the proton-magnetization spin-lattice recovery functions after a saturating pulse sequence were measured in phases I, II, and III of powdered ${\mathrm{CsHSO}}_{4},$ and the corresponding stretched exponents and the proton ${T}_{1},$ ${T}_{1\ensuremath{\rho}},$ and ${T}_{2}$ parameters were determined. The recovery of the proton magnetization in the spin-lattice relaxation time experiment is nonexponential in phases I and II, but becomes monoexponential in the high-temperature fast-ion conducting phase III. The observed value of the stretched exponent $\ensuremath{\alpha}\ensuremath{\sim}0.5$ in phases I and II proves the existence of a local-polarization distribution function characteristic for orientational glasses and the presence of random fields or random bonds.

Phase transitions in disordered systems: Exactly solvable model

The critical behavior at phase transitions of random systems is studied within the framework of an exactly solvable model which takes into account interactions of fluctuations with equal and opposite momenta. Using the replica method, the dimensional reduction by 2 for the φ4 model with a quenched random field is explicitly shown. Phase transitions in systems with two interacting order parameters which in addition are coupled to two independent random fields are also studied. In the absence of random fields the model demonstrates fluctuation induced phase transitions of the first order for spacial dimension d<4. In random systems with only one quenched random field present, second order phase transitions are restored. Two random fields suppress any phase transitions for d<4. For interaction of an infinite range, the model demonstrates the mean field critical asymptotics independently of dimensionality or the presence of random fields.

Fluctuation effects in the Ising model with reduced interaction and quenched disorder.

The effect of quenched random fields and local perturbations of critical temperature on the critical behavior at phase transitions is studied within the framework of an exactly solvable model that takes into account interaction of fluctuations with equal and opposite momenta. Using the replica method the dimensional reduction by 2 for systems with finite-range interaction and quenched random fields is explicitly shown. For interaction of the infinite range the model demonstrates the mean-field critical asymptotics independently of dimensionality or the presence of random fields. \textcopyright{} 1996 The American Physical Society.

Random-field effects in critical phenomena. Exactly solvable model

The effect of quenched random fields on the critical behavior at phase transitions is studied within the framework of an exactly solvable model that takes into account interaction of fluctuations with equal and opposite momenta and belongs to the universality class of the spherical model. Using the replica method the dimensional reduction by 2 for systems with finite-range interaction is explicitly shown. For interaction of the infinite range the model demonstrates the mean field critical asymptotics independently of dimensionality or the presence of random fields.

Effects of a Gaussian random field in the Sherrington-Kirkpatrick spin glass.

The infinite-range Ising spin glass in the presence of a Gaussian random field is investigated by means of the replica method. The replica-symmetric solution and its instability are discussed; it is shown that the Almeida-Thouless instability regions are always reduced by the random field. The crossover exponent \ensuremath{\varphi} associated with the irreversibility line is shown to be nonuniversal in the presence of a random field, varying in a range from 1 to 3. Some of our results are compared with recent experimental measurements performed in the diluted antiferromagnet ${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{F}}_{2}$.

Dielectric study of Rb0.75(ND4)0.25D2AsO4

The complex dielectric constant of Rb0.75(ND4)0.25D2AsO4 along the tetragonal crystallographic c axis has been measured as a function of temperature for frequencies between 100 Hz and 1 MHz. The dielectric relaxation is described using a Frohlich-type distribution function. The expressions for epsilon ' and epsilon " are evaluated on this basis and fitted to the experimental data. The characteristic central frequency fepsilon obeys an Arrhenius law and the relaxation process is polydispersive. Below the freezing temperature Tf=68.9 K the dielectric intensity epsilon (0)- epsilon ( infinity ) is decreasing with decreasing temperature and its temperature dependence can be described by the replica-symmetry-breaking solution of the infinite range Ising spin glass model in the presence of random fields.

The d-dimensional sine-Gordon model in the presence of random fields

We study the properties of a d-dimensional sine-Gordon model in the presence of a random field that couples linearly to the sine-Gordon field using the Wilson renormalization group approach via the replica trick. No stable fixed point is found for dimensionalities d<4, corresponding to the absence of long-range order. Such a situation seems to occur in experiments on impurity-pinned charge-density-wave systems in which a “glassy behaviour” appears to be induced by arbitrarily weak symmetry-breaking randomness.

Fractal measures of diffusion in the presence of random fields.

We study diffusion in a linear chain where random fields are located at each site and can accept the values \ifmmode\pm\else\textpm\fi{}E with equal probability. While the average density distribution of a random walker scales and is described by a single exponent, it requires an infinite hierarchy of exponents \ensuremath{\alpha} to characterize the fluctuations. Their density distribution f(\ensuremath{\alpha}) is a single-hump function and depends continuously on the magnitude of the field E.

Diffusion in the presence of random fields in d⩾2 dimensions

The authors study diffusion in the presence of random fields in d-dimensional systems. They find an exact upper bound for the mean-square displacement (R2)≤n2 nu where nu is the self-avoiding walk end-to-end exponent. They also present numerical results in two dimensions which indicate normal diffusion for d≥2. This is consistent with the above exact bound.

On the field dependence of random walks in the presence of random fields

Numerical simulations and scaling arguments are used to study the field dependence of a random walk in a one-dimensional system with a bias field on each site. The bias is taken randomly with equal probability to be +E or −E. The probability density¯P(x, t) is found to scale asymptotically as $$\left\{ {[A(E)]^{\beta /2} /\ln ^2 t} \right\}\exp \left( { - \left\{ {x[A(E)]^{\beta /2} /\ln ^2 t} \right\}^\alpha } \right)$$ withA(E)=ln[(1+E)/(1-E)],β=4.25, and α=1.25. The mean square displacement scales as\(\langle x^2 \rangle \sim [A(E)]^{ - \beta } F[tA^\beta (E)]\), where F(u)∼ln4u asymptotically.

Diffusion in the presence of random fields and transition rates: Effect of the hard-core interaction.

Diffusion in the presence of random fields and transition rates: Effect of the hard-core interaction.

Random-field smearing of the proton-glass transition.

Within a replica-symmetric mean-field theory we have studied the proton pseudo-spin-glass behavior of a random-bond classical Ising system in a homogeneous transverse field \ensuremath{\Omega} and a random longitudinal field. This model is expected to describe some properties of the mixed hydrogen-bonded ferro- and antiferroelectric crystals such as ${\mathrm{Rb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{NH}}_{4}$${)}_{\mathit{x}}$${\mathrm{H}}_{2}$${\mathrm{PO}}_{4}$ which have recently been investigated experimentally. It is shown that in the presence of Gaussian random fields with zero mean and variance \ensuremath{\Delta} the proton-glass transition is smeared out, i.e., the cusp in the dielectric susceptibility is rounded off and the proton-glass order parameter remains finite at temperatures above the nominal freezing temperature. However, the average dielectric polarization is strictly zero for a symmetric bond distribution. We have also determined the limits of stability of the replica-symmetric solution for the case of a deuterated system (\ensuremath{\Omega}=0). The replica-symmetric proton-glass phase is separated from the phase with broken replica symmetry by a line of instability in the (T,\ensuremath{\Delta}) plane. The crossing of this line is thus connected with a phase transition which persists in the presence of random fields. Finally, the distribution function of local parallel fields P(h) determining the magnetic resonance line shape has been calculated within the random-field model and the results applied to interpret some recent experimental data.

The Random-Field Ising Model: A Free Energy Study

Thermodynamic properties of the random-field Ising model are reviewed and compared with published experimental results on diluted antiferromagnets in a uniform field. The Landau-Ginzburg free energy is calculated in the self-consistent approximation for 3-dimensional systems treating the random field induced fluctuations and the thermodynamic fluctuations of the order parameter separately. At low temperatures and in the presence of random fields two states exist, the stable, long-range ordered state, and the metastable disordered microdomain state. In a heating process, the ordered state changes to the high-temperature phase at the well defined transition temperature. The transition is first order for arbitrarily weak random field. Critical properties are briefly examined and according to the Ginzburg criterion, the classical critical behaviour is predicted for large random fields. For weak fields, nonclassical critical behaviour is expected.

Phase transitions and metastable states in the presence of random fields

The application of a uniform magnetic field to a diluted Ising antiferromagnet produces a random staggered field and so can be used to study the random field Ising model. In this paper we describe neutron scattering measurements on Mn x Zn 1− x F 2. They show that at low temperatures there are many metastable states which are all stable for experimentally accessible times. There is a sharp boundary in the H/T plane which separates metastability from ergodicity. The critical phenomena close to this metastability boundary is discussed.

Quantum and random-field fluctuations in the SU Schrieffer-Heeger model-a renormalisation group study in the 1/N expansion

The effects of quantum and random-field fluctuations are investigated. The authors investigate within one theory the crossover from M=0 to M= infinity (M is the ionic mass) in the presence of random fields. They find that random fields can close the Peierls gap. A new gap (similar to the spin glass order parameter) is defined. This gap describes the local Peierls distortion which may explain the Raman spectrum in trans-(CH)x.