Local and cluster critical dynamics of the 3d random-site Ising model

We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L=10-96 are analysed by a finite-size-scaling technique. The site dilution concentration p=0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.Comment: 24 pages, 16 figures, style file include

High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions

In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the \sus and the free energy are obtained for the quenched bond-diluted Ising model in $d = 3$--5 dimensions. They are analysed using different extrapolation methods tailored to the expected singularity behaviours. In $d = 4$ and 5 dimensions we confirm that the critical behaviour is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in $d = 4$ is confirmed and our results for the critical behaviour of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation and random fixed point. We estimate the critical exponent of the \sus to be $\gamma =1.305(5)$ at the random fixed point.Comment: 16 pages, 10 figure

Billion-atom Synchronous Parallel Kinetic Monte Carlo Simulations of Critical 3D Ising Systems

An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm developed by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors time clocks current in a global sense. Boundary conflicts are rigorously solved by adopting a chessboard decomposition into non-interacting sublattices. We find that the bias introduced by the spatial correlations attendant to the sublattice decomposition is within the standard deviation of the serial method, which confirms the statistical validity of the method. We have assessed the parallel efficiency of the method and find that our algorithm scales consistently with problem size and sublattice partition. We apply the method to the calculation of scale-dependent critical exponents in billion-atom 3D Ising systems, with very good agreement with state-of-the-art multispin simulations

Computer simulation of the critical behavior of 3D disordered Ising model

The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.Comment: 14 RevTeX pages, 6 figure

Relaxational dynamics in 3D randomly diluted Ising models

We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z=2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from T=\infty to T=T_c. In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z=2.35(2).Comment: 38 page

Magnetostriction in the magneto-sensitive elastomers with inhomogeneously magnetized particles: pairwise interaction approximation

We analyze the magnetostriction effect occurring in the magneto-sensitive elastomers (MSEs) containing inhomogeneously magnetized particles. As it was shown before, the expression for the interaction potential between two magnetic spheres, that accounts for their mutual inhomogeneous magnetization, can be obtained from the Laplace equation. We use this potential in the approximation formula form to construct magnetic energy of the sample in terms of the pairwise interactions of the particles. We show that this form of magnetic energy leads to the same demagnetizing factor as predicted by the continuum mechanics, confirming that only dipole-dipole magnetic interactions are important on a large scale. As the next step, we examine the role played by the particles arrangement on the magnetostriction effect. We consider different spatial distributions of the magnetic particles: a uniform one, as well as several lattice-type distributions (SC, BCC, HCP and FCC arrangements). We show that the particles arrangement affects significantly the magnetostriction effect if the separation between them became comparable with the particles' dimensions. We also show that, typically, this contribution to the magnetostriction effect is of the opposite sign to the one related with the initial elastomer shape. Finally, we calculate the magnetostriction effect using the same interaction potential but expressed in a form of a series expansion, qualitatively confirming the above findings