Static critical behavior of the random field Ising model

A. Malakis, Nikolaos G. Fytas

Jacques Villain, Thomas Nattermann, Moshe Schwartz

Pasquale Calabrese, Andrea Pelissetto C, Ettore Vicari

We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.

David Peter Belanger

New advances in experiments on the random-field Ising model, as realized in dilute antiferromagnets, have brought us much closer to a full characterization of the static and dynamic critical behavior of the unusual phase transition in three dimensions (d=3). The most important experiments that have laid the ground work for our present understanding are reviewed. Comparisons of the data with Monte Carlo simulations of the d=3 critical behavior are made. We review the current experimental understanding of the destroyed d=2 transition and the experiments exploring the d=2 metastability at low T. Connections to theories most relevant to the interpretations of all the experiments are discussed.

Nikolaos G. Fytas, Panagiotis E. Theodorakis, Ioannis Georgiou +1 more

Joaquín Marro, A. Labarta, Javier Tejada

A Monte Carlo analysis of the ferromagnetic spin-1/2 Ising model with nearest-neighbor interactions and static (quenched) site dilution, where a fraction x, 0\ensuremath{\le}x\ensuremath{\le}0.2, of the spins in a simple-cubic lattice are randomly replaced by vacant sites, reveals effective critical exponents varying continuously with x.