arXiv subjects

H. Rieger

Publications and source records attributed to H. Rieger.

62 records · Page 4Linked to original sources

arXiv1995

A Numerical Study of the Random Transverse-Field Ising Spin Chain

We study numerically the critical region and the disordered phase of the random transverse-field Ising chain. By using a mapping of Lieb, Schultz and Mattis to non-interacting fermions, we can obtain a numerically exact solution for rather large system sizes, $L \le 128$. Our results confirm the striking predictions of earlier analytical work and, in addition, give new results for some probability distributions and scaling functions.

cond-mat↗

arXiv1995

Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models

The low temperature dynamics of the two- and three-dimensional Ising spin glass model with Gaussian couplings is investigated via extensive Monte Carlo simulations. We find an algebraic decay of the remanent magnetization. For the autocorrelation function $C(t,t_w)=[< S_i(t+t_w)S_i(t_w)>]_{av}$ a typical aging scenario with a $t/t_w$ scaling is established. Investigating spatial correlations we find an algebraic growth law $ξ(t_w)\sim t_w^{α(T)}$ of the average domain size. The spatial correlation function $G(r,t_w)=[< S_i(t_w)S_{i+r}(t_w)>^2]_{av}$ scales with $r/ξ(t_w)$. The sensitivity of the correlations in the spin glass phase with respect to temperature changes is examined by calculating a time dependent overlap length. In the two dimensional model we examine domain growth with a new method: First we determine the exact ground states of the various samples (of system sizes up to $100\times 100$) and then we calculate the correlations between this state and the states generated during a Monte Carlo simulation.

cond-mat↗

arXiv1994

Monte Carlo Studies of Ising Spin Glasses and Random Field Systems

We review recent numerical progress in the study of finite dimensional strongly disordered magnetic systems like spin glasses and random field systems. In particular we report in some details results for the critical properties and the non-equilibrium dynamics of Ising spin glasses. Furthermore we present an overview over recent investigations on the random field Ising model and finally of quantum spin glasses.

cond-mat↗

arXiv1994

Fluctuation Dissipation Ratio in Three-Dimensional Spin Glasses

We present an analysis of the data on aging in the three-dimensional Edwards Anderson spin glass model with nearest neighbor interactions, which is well suited for the comparison with a recently developed dynamical mean field theory. We measure the parameter $x(q)$ describing the violation of the relation among correlation and response function implied by the fluctuation dissipation theorem.

cond-mat↗

arXiv1994

Random bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

We investigate the zero-temperature quantum phase transition of the random bond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter-- and correlation function--probability distribution show a nontrivial scaling near the critical point which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.

cond-mat↗

arXiv1994

Reentrant Behavior in the Domany-Kinzel Cellular Automaton

We present numerical and analytical results for a special kind of one-dimensional probabilistic cellular automaton, the so called Domany-Kinzel automaton. It is shown that the phase boundary separating the active and the recently found chaotic phase exhibits reentrant behavior. Furthermore exact results for the $p_2$=0-line are discussed.

hep-lat↗

arXiv1992

Number of solutions of the TAP equations for p--spin interaction spin glasses

The number $\langle N_s\rangle$ of solutions of the equations of Thouless, Anderson and Palmer for p--spin interaction spin glass models is calculated. Below a critical temperature $T_c$ this number becomes exponentially large, as it is in the SK--model ($p=2$). But in contrast to this, for any $p>2$ the factor $α(T)=N^{-1} \ln\langle N_s\rangle$ jumps discontinuously at $T_c(p)$, which is consistent with the discontinuity occuring within the mean--field theory for these models. For zero temperature the results obtained by Gross and Mézard are reproduced, and for $p\rightarrow\infty$ one gets the result for the random energy model.

cond-mat↗

arXiv1992

Fast vectorized algorithm for the Monte Carlo Simulation of the Random Field Ising Model

An algoritm for the simulation of the 3--dimensional random field Ising model with a binary distribution of the random fields is presented. It uses multi-spin coding and simulates 64 physically different systems simultaneously. On one processor of a Cray YMP it reaches a speed of 184 Million spin updates per second. For smaller field strength we present a version of the algorithm that can perform 242 Million spin updates per second on the same machine.

hep-lat↗