Experimental Characterization of the Ising Model in Disordered Antiferromagnets

The current status of experiments on the d=2 and d=3 random-exchange and random-field Ising models, as realized in dilute anisotropic antiferromagnets, is discussed. Two areas of current investigation are emphasized. For d=3, the large random field limit is being investigated and equilibrium critical behavior is being characterized at high magnetic concentrations.Comment: 19 pages, 7 figures, Ising Centennial Colloquium, to be published in the Brazilian Journal of Physic

Experiments on the random field Ising model

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.Comment: 25 pages, 5 figures, LaTeX, to be published in World Scientific "Spin Glasses and Random Fields", ed. A. P. Youn

Equilibrium random-field Ising critical scattering in the antiferromagnet Fe(0.93)Zn(0.07)F2

It has long been believed that equilibrium random-field Ising model (RFIM) critical scattering studies are not feasible in dilute antiferromagnets close to and below Tc(H) because of severe non-equilibrium effects. The high magnetic concentration Ising antiferromagnet Fe(0.93)Zn(0.07)F2, however, does provide equilibrium behavior. We have employed scaling techniques to extract the universal equilibrium scattering line shape, critical exponents nu = 0.87 +- 0.07 and eta = 0.20 +- 0.05, and amplitude ratios of this RFIM system.Comment: 4 pages, 1 figure, minor revision

The random field critical concentration in dilute antiferromagnets

Monte Carlo techniques are used to investigate the equilibrium threshold concentration, xe, in the dilute anisotropic antiferromagnet Fe(x)Zn(1-x)F2 in an applied magnetic field, considered to be an ideal random-field Ising model system. Above xe equilibrium behavior is observed whereas below xe metastability and domain formation dominate. Monte Carlo results agree very well with experimental data obtained using this system.Comment: 9 pages, 3 figure

Far infrared spectroscopy on the three-dimensional dilute antiferromagnet Fe(x)Zn(1-x)F2

Fourier-transform Infrared (FT-IR) Spectroscopy measurements have been performed on the three-dimensional dilute antiferromagnet Fe(x)Zn(1-x)F2 with x=0.99 ~ 0.58 in far infrared (FIR) region. The FIR spectra are analyzed taking into account the ligand field and the local exchange interaction probability with J1 ~ J3; |J1|,|J3|<<|J2|, where J1, J2 and J3 are the nearest neighbor, second nearest neighbor and third nearest neighbor exchange interaction constants, respectively. The concentration dependence of the FIR spectra at low temperature is qualitatively well reproduced by our analysis, though some detailed structure remains unexplained.Comment: 10 pages, 3 figure

Universal aging properties at a disordered critical point

We investigate, analytically near the dimension $d_{uc}=4$ and numerically in $d=3$, the non equilibrium relaxational dynamics of the randomly diluted Ising model at criticality. Using the Exact Renormalization Group Method to one loop, we compute the two times $t,t_w$ correlation function and Fluctuation Dissipation Ratio (FDR) for any Fourier mode of the order parameter, of finite wave vector $q$. In the large time separation limit, the FDR is found to reach a non trivial value $X^{\infty}$ independently of (small) $q$ and coincide with the FDR associated to the the {\it total} magnetization obtained previously. Explicit calculations in real space show that the FDR associated to the {\it local} magnetization converges, in the asymptotic limit, to this same value $X^{\infty}$. Through a Monte Carlo simulation, we compute the autocorrelation function in three dimensions, for different values of the dilution fraction $p$ at $T_c(p)$. Taking properly into account the corrections to scaling, we find, according to the Renormalization Group predictions, that the autocorrelation exponent $\lambda_c$ is independent on $p$. The analysis is complemented by a study of the non equilibrium critical dynamics following a quench from a completely ordered state.Comment: 8 pages, 5 figure

Analysis of wasp-waisted hysteresis loops in magnetic rocks

The random-field Ising model of hysteresis is generalized to dilute magnets and solved on a Bethe lattice. Exact expressions for the major and minor hysteresis loops are obtained. In the strongly dilute limit the model provides a simple and useful understanding of the shapes of hysteresis loops in magnetic rock samples.Comment: 11 pages, 4 figure