Strength Of Random Field Research Articles

Single-crystal neutron-diffraction study of the orientational glass state of (NaCN)1-x(KCN)x.

Single crystals of (NaCN${)}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(KCN${)}_{\mathit{x}}$ with concentrations x=0.19, 0.44, and 0.89 have been investigated by elastic neutron diffraction. The mixed crystals with x=0.19 and 0.44 exhibit a transition to an orientational glass state, while those with x=0.89 transform into a coexistence region of cubic and rhombohedral phases. Diffuse scattered intensities have been studied as a function of temperature T, phonon wave vector q, and momentum transfer Q. I(T,q,Q) provides insight into the character of the freezing process. From a detailed analysis of the structure factors, the orientational distribution of the CN molecules was determined. With increasing strength of random fields, 〈100〉 orientations are favored.

Plane‐wave scattering from a random fluid half‐space

An integrodifferential equation method is applied to low‐frequency plane‐wave scattering by a random fluid half‐space. The results of coherent reflection of a plane wave from a random fluid half‐space have been previously reported [J. Acoust. Soc. Am. Suppl. 1 85, S70 (1989)]. In this paper, the random scattered field strength is calculated, assuming that the random sound‐speed correlation function has independent correlation lengths along the vertical and horizontal directions. Numerical results obtained using this approach are compared to those obtained using the Born approximation. They show that the coherent energy loss due to scattering cannot be ignored at low frequencies, since the coherent wave can propagate to large depths in the random medium. This study has potential application to the understanding of ocean bottom reverberation problems.

Quadrupolar relaxation in (KBr)1-x(KCN)x.

Brillouin scattering was used to study the dynamic properties of the mixed crystals (KBr${)}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$(KCN${)}_{\mathrm{x}}$. By analyzing the frequencies and linewidths of the ${T}_{2g}$-symmetry phonon, we were able to determine the cyanide quadrupolar relaxation rate as a function of temperature in the paraelastic regime. We found that this relaxation frequency is proportional to exp(-1/T), rather than proportional to the square root of temperature (\ensuremath{\surd}T ), as assumed in Michel's random-field theory. Modifying this theory by incorporating the observed temperature dependence of the relaxation rate improves the agreement with experimental data but is still not adequate. The hierarchically constrained relaxation model of Palmer et al., on the other hand, does provide a phenomenological explanation for our data. In addition, we have determined the value of the random-field strength in these mixed systems.

Heisenberg-to-Ising crossover in a random-field model with uniaxial anisotropy.

Uniaxial anisotropy causes a crossover between Ising and Heisenberg behavior in a random-field model. At random-field strengths and dimensionalities, intermediate between those which give either the Ising and Heisenberg domain states, a new ``boundary'' domain state appears. A novel criterion is also derived for domain-boundary roughening in the Heisenberg limit. The two-dimensional version of this model can be applied to ferromagnetic-antiferromagnetic sandwiches with interface randomness and leads to a prediction of an exchange anisotropy effect below a critical thickness of order the domain-wall width, and an enhancement of this effect below a second critical thickness.

The Random Field Ising Model in 2 + ϵ Dimensions Critical Behaviour from Interface Fluctuations

AbstractThe critical behaviour of the random field Ising model is calculated in d = 2 + ϵ dimensions, using previous findings on interface roughening of Grinstein and Ma. The critical exponents are expressed in terms of ϵ and the dimension β/v of the order parameter field. ϵ and β/v are assumed to be small. For nonvanishing random field strength HR the critical behaviour is governed by a zero temperature fixed point HRc ˜ (ϵ + 2β/v)3/4. In particular μ = 3/4 and v−1 = ⅔ (ϵ + 2β/v) are obtained for the interface tension and the correlation length exponent, respectively. The relation between interface and bulk correlation lengths in the various regions is discussed.

Two-dimensional XY model in a random uniaxial field.

We present a low-temperature analysis of the two-dimensional XY model in the presence of a random uniaxial field, which points in the \ifmmode\pm\else\textpm\fi{}x directions with equal probability. We first construct a domain argument, valid at zero temperature in all dimensions, which indicates that in all dimensions the ground state is ferromagnetic, for small field, and the magnetization points in the y direction. We then construct Kosterlitz-style recursion relations for this model in two dimensions. Analyzing these equations, we find an ordered phase with Ising symmetry at nonzero temperature and small values of the random-field strength. Thus, the random field induces long-range order in a system which exhibits only quasiorder in its pure state. We also consider the p-state generalization of the model, and find an ordered phase with 2p-fold symmetry at nonzero temperature. Our results are in disagreement with earlier work by Dotsenko and Feigelman, who found a paramagnetic phase at low temperatures.

The Potts model in a random field: a Monte Carlo study

The three-state Potts model in three dimensions in the presence of a random field has been investigated by Monte Carlo simulation. For a range of values of the random field strengths, results for the internal energy and order parameter are consistent with the existence of a first-order phase transition to a ferromagnetic state.

Numerical results for the random field Ising model (invited)

We have performed numerical calculations for the random field (H) ferromagnetic Ising model in two dimensions. To study equilibrium properties, we have used the transfer matrix technique, thus bypassing serious equilibration problems which would arise in a Monte Carlo calculation for random systems. We have calculated the structure factor S vs H. Our results are consistent with S∼exp(c/H2) as predicted by theories which yield a lower critical dimension dc=2, whereas the expected behavior for dc=3, S∼H−4, is inconsistent with our results. To study dynamic properties we have used Monte Carlo simulations to determine the equilibration of Ising systems in random fields at low temperatures T following a quench from high T. The rate at which domains grow with time is determined as a function of the random field strength H, the linear dimension of the system L and temperature T. Domains are found to grow logarithmically with time. For small systems, L≤L*=(4J/H)2, the exponents a and b of the exponential equilibration time τ∼exp[(H/T)aLb] are found to be a≂1.0 and b≂0.5, in agreement with recent calculations based on approximate interface models. We tested the L and H/T dependence of τ in 3D and found a≂1.0, b≂0.5 also in 3D.

Monte Carlo study of the equilibration of the random-field Ising model.

Monte Carlo simulations are used to study the equilibration of Ising systems in random magnetic fields at low temperatures (T) following a quench from high T in two dimensions. The rate at which domains grow with time is determined as a function of the random-field strength H, the linear dimension of the system L, and temperature T. Domains are found to grow logarithmically with time. For small systems L${L}^{\mathrm{*}}$=(4J/H${)}^{2}$, the exponents a and b of the exponential equilibration time \ensuremath{\tau}\ensuremath{\sim}exp[(H/T${)}^{a}$${L}^{b}$] are found to be a\ensuremath{\simeq}1.0, b\ensuremath{\simeq}0.5 in agreement with recent calculations based on approximate interface models. We tested the L and H/T dependence of \ensuremath{\tau} in three dimensions for L${L}^{\mathrm{*}}$ and found a\ensuremath{\simeq}1.0 and b\ensuremath{\simeq}0.5 also in three dimensions.

Random-field Ising model on a Bethe lattice

The ground state of the random-field Ising ferromagnet on a Bethe lattice is found. With decreasing random-field strength an infinite series of spin-flip transitions precedes the onset of ferromagnetism. The $T=0$ critical behavior is not mean-field-like. At finite temperatures a series of Griffiths singularities precedes the phase transition. As $T\ensuremath{\rightarrow}0$, the Griffiths singularities terminate at the spin-flip transitions. The $T\ensuremath{\ne}0$ critical behavior is argued to be mean-field-like.

Equilibration of random-field Ising systems

The equilibration of Ising systems in random magnetic fields at low temperatures ($T$) following a quench from high $T$ is studied in the framework of a simple solid-on-solid model. The rate at which ordered domains in the model grow with time in any dimension ($d$) is estimated as a function of the random-field strength, the exchange strength, and $T$, on the basis of an approximate analogy to the problem of a one-dimensional random walk in a random medium. Domains are argued to grow logarithmically with time for all $d$. This result has a simple interpretation in terms of energy barriers which must be surmounted in the equilibration process.

Interface Motion and Nonequilibrium Properties of the Random-Field Ising Model

The dynamics of a continuum interface model in a random medium are studied and the results applied to the random-field Ising model. We find that if the dimensionality $d<5$, the interface will move only if a force beyond a finite depinning threshold ${F}_{c}\ensuremath{\sim}{h}^{\frac{4}{(5\ensuremath{-}d)}}$ is applied, where $h$ is the random field strength. Thus, when the random-field Ising model is quenched to low temperatures, there is a critical value ${R}_{c}\ensuremath{\sim}\frac{1}{{h}^{\frac{4}{(5\ensuremath{-}d)}}}$ for the average radius of curvature $R$ of the domain walls. If $R>{R}_{c}$, the domain structure is frozen. If $R<{R}_{c}$, the domain structure evolves until $R\ensuremath{\sim}{R}_{c}$.

Renormalized Field Theory of Quenched System under Gaussian Random Fields Conjugate to Anisotropic Spin Fields

The effects of Gaussian random fields applied only to the m spin fields of the anisotropic (n+m)-vector model are studied in the quenched case via the renormalized rp' field theory by examining the stability of four fixed points and one fixed line in the large n and m limits. Regardless of the value of n/m, only a decoupled case is infrared stable, so that random fields prove to have no effects on the critical properties (e.g., critical indices) of the pure n spin fields. In such a decoupled case, as far as random fields are weak, longitudinal order corresponding to a random fixed point is observed remarkably. However, as the strength of random fields grows stronger, random fixed point moves to a Gaussian (trivial) fixed point and in consequence only transverse order gets conspicuous. The above. results are physically consistent with Aharony's arguments.

Computer simulation of the velocity diffusion of cosmic rays

Monte Carlo simulation experiments have been performed in order to study the velocity diffusion of charged particles in a static turbulent magnetic field. By following orbits of particles moving in a large ensemble of random magnetic field realizations with suitably chosen statistical properties, a pitch-angle diffusion coefficient is derived. Results are presented for a variety of particle rigidities and rms random field strengths and compared with the predictions of standard quasi-linear theory and the nonlinear partially averaged field theory.

A Rigorous Cosmic-Ray Transport Equation with no Restrictions on Particle Energy

view Abstract Citations (46) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Rigorous Cosmic-Ray Transport Equation with no Restrictions on Particle Energy Klimas, A. J. ; Sandri, G. Abstract A new transport equation for the cosmic-ray omnidirectional intensity is obtained. This equation follows exactly from the coupled pair of differential moment equations we presented earlier. It can be characterized as a nonlocal convection-diffusion equation in which the usual transport coefficients are replaced by time integral operators. The nonlocal equation is shown to reduce to the standard convection-diffusion form if the adiabatic approximation can be applied. In general, the adiabatic approximation does not apply; however, by going to the limits of infinite and zero gyroradius and, in addition, applying the adiabatic approximation, the large- and small-gyroradius transport theories due originally to Jokipii are regained. The validity of these theories as asymptotic limits and as approximate theories in the interplanetary magnetic field is discussed. It is concluded that the small-gyroradius limit cannot be considered an approximate theory for low-energy particles even when the random field strength is weak. In addition, by scaling the length and time appropriately, a low-energy scaling law is derived. This law can be used to obtain low rigidity solutions to the nonlocal convection-diffusion equation. Thus, the nonlocal convection-diffusion equation can be used to study solar-modulation or solar-particle event phenomena down to arbitrarily low rigidities, provided the particle distribution function is nearly isotropic. Subject headings: cosmic rays - hydromagnetics - interplanetary medium Publication: The Astrophysical Journal Pub Date: March 1973 DOI: 10.1086/152018 Bibcode: 1973ApJ...180..937K full text sources ADS |