A Self-Consistent Ornstein–Zernike Approximation for the Random Field Ising Model

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

Effects of the randomly distributed magnetic field on the phase diagrams of Ising nanowire I: Discrete distributions

We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent gamma. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for gamma<3. On the other hand, the spins undergo a phase transition from an ordered phase to a disordered phase as the dispersion of the random fields increases for gamma>3. The phase transition may be either continuous or discontinuous depending on the shape of the random field distribution. We derive the condition for the nature of the phase transition. Numerical simulations are performed to confirm the results.

We calculate correlation radius of polarization fluctuations in the disordered ferroelectrics. The consideration is performed in the model suitable for relaxor ferroelectrics. We consider reference Burns phase in a mean field approximation subjected to random electric field E. The “entire relaxor” is then obtained by averaging of characteristics of the reference phase with distribution function of the random field. For correlation radius (Rc) calculation we take into account the damping of the reference phase soft mode and its dependence on E and perform the averaging over the random field distribution. The obtained temperature dependence of Rc is shown to be strongly dependent on the decay parameter. It appears to be completely different for the disordered system either in the dipole-glass state or in mixed ferroglass phase. The fitting of calculated and measured Rc(T) in PbMg1/3Nb2/3O3 is performed.

The random field Ising model with four spin interactions is studied within the finite cluster approximation (F.C.A), on square and simple cubic lattices. We have investigated the influence of the four spin interactions on the phase diagrams of the system. We have shown that for the simple cubic lattice, the tricritical behaviour due to the random field does not exist for every strength of the four spin interactions, and that he tricritical point due to four spin intenactions disappears when the value of the random field is large.

Generalizing the Affine Framework to HJM and Random Field Models

We develop multispectral random field image models for use in image processing applications. The simultaneous autoregressive and Markov random field (MRF) models have been widely used in modeling intensity images. In this work we extend these models to include the more general multispectral case where images are represented by multiple intensity planes. In particular, we focus on the obvious application to color texture modeling using the RGB color model. For each model type we present the model equations, develop methods for synthesizing images based on these models and procedures for estimating the model parameters. In addition, the conditions necessary to ensure model validity are identified. We also provide experimental results which, substantiate the validity of these results. Color images synthesized from these models are shown to have the statistical characteristics implied by the model equations and parameters estimated from these images are very close to the known values from which the images were generated. In further experiments color random field models were fitted to natural texture samples. Images synthesized from these models are observed to be visually similar to the original images.

Convex relaxation for IMSE optimal design in random-field models

We study the ground-state (T=0) morphologies in the d=3 random-field Ising model (RFIM) using a computationally efficient graph-cut method. We focus on paramagnetic states which arise for disorder strengths Δ>Δc, where Δc is the critical disorder strength at T=0. These paramagnetic states consist of correlated “domains” of up and down spins which are separated by rough, fractal interfaces. They show novel scattering properties with a cusp singularity in the correlation function at short distances.

For Abstract see ChemInform Abstract in Full Text.

We determine the phase diagram of the transverse Ising model with a trimodal distribution (sum of three \ensuremath{\delta} functions) for a longitudinal random field at T=0, using a mean-field approximation. The phase diagram includes tricritical points, ordered critical points, a fourth-order point, critical end points, and a double critical end point. Our T=0 phase diagram is completely equivalent to the one obtained by Kaufman, Klunzinger, and Khurana for the random-field Ising model. We show that the temperature and the magnitude of the transverse field play a similar role.

A theoretical study of the spin- [formula omitted] Ising model in a random field with crystal field

A theoretical study of the spin- [formula omitted] Ising model in a random field with crystal field

Modeling of non-stationary random field of undrained shear strength of soil for slope reliability analysis

Bayesian hierarchical models usually model the risk surface on the same arbitrary geographical units for all data sources. Poisson/gamma random field models overcome this restriction as the underlying risk surface can be specified independently to the resolution of the data. Moreover, covariates may be considered as either excess or relative risk factors. We compare the performance of the Poisson/gamma random field model to the Markov random field (MRF)-based ecologic regression model and the Bayesian Detection of Clusters and Discontinuities (BDCD) model, in both a simulation study and a real data example. We find the BDCD model to have advantages in situations dominated by abruptly changing risk while the Poisson/gamma random field model convinces by its flexibility in the estimation of random field structures and by its flexibility incorporating covariates. The MRF-based ecologic regression model is inferior. WinBUGS code for Poisson/gamma random field models is provided.