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

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

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.Comment: 13 pp., HLRZ 53/9

Critical dynamics of diluted relaxational models coupled to a conserved density (diluted model C)

We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a non-conserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics, however it is the effective critical behavior which is often observed in experiments and in computer simulations and this is described by the full set of dynamical equations of diluted model C. Indeed different scenarios of effective critical behavior are predicted.Comment: 4 pages, 5 figure

Static and dynamic structure factors in three-dimensional randomly diluted Ising models

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.Comment: 43 page

Ferrimagnetism of dilute Ising antiferromagnets

It is shown that nearest-neighbor antiferromagnetic interactions of identical Ising spins on imbalanced bipartite lattice and imbalanced bipartite hierarchical fractal result in ferrimagnetic order instead of antiferromagnetic one. On some crystal lattices dilute Ising antiferromagnets may also become ferrimagnets due to the imbalanced nature of the magnetic percolation cluster when it coexists with the percolation cluster of vacancies. As evidenced by the existing experiments on $Fe_pZn_{1-p}F_2$, such ferrimagnetism is inherent property of bcc lattice so thermodynamics of these compounds at low $p$ can be similar to that of antiferromagnet on imbalanced hierarchical fractal.Comment: 6 pages, 4 figure

Scaling properties of the critical behavior in the dilute antiferromagnet Fe(0.93)Zn(0.07)F2

Critical scattering analyses for dilute antiferromagnets are made difficult by the lack of predicted theoretical line shapes beyond mean-field models. Nevertheless, with the use of some general scaling assumptions we have developed a procedure by which we can analyze the equilibrium critical scattering in these systems for H=0, the random-exchange Ising model, and, more importantly, for H>0, the random-field Ising model. Our new fitting approach, as opposed to the more conventional techniques, allows us to obtain the universal critical behavior exponents and amplitude ratios as well as the critical line shapes. We discuss the technique as applied to Fe(0.93)Zn(0.07)F2. The general technique, however, should be applicable to other problems where the scattering line shapes are not well understood but scaling is expected to hold.Comment: 17 pages, 5 figure

Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors

We study the nature of the multicritical point in the three-dimensional O(3)+O(2) symmetric Landau-Ginzburg-Wilson theory, which describes the competition of two order parameters that are O(3) and O(2) symmetric, respectively. This study is relevant for the SO(5) theory of high-Tc superconductors, which predicts the existence of a multicritical point in the temperature-doping phase diagram, where the antiferromagnetic and superconducting transition lines meet. We investigate whether the O(3)+O(2) symmetry gets effectively enlarged to O(5) approaching the multicritical point. For this purpose, we study the stability of the O(5) fixed point. By means of a Monte Carlo simulation, we show that the O(5) fixed point is unstable with respect to the spin-4 quartic perturbation with the crossover exponent $\phi_{4,4}=0.180(15)$, in substantial agreement with recent field-theoretical results. This estimate is much larger than the one-loop $\epsilon$-expansion estimate $\phi_{4,4}=1/26$, which has often been used in the literature to discuss the multicritical behavior within the SO(5) theory. Therefore, no symmetry enlargement is generically expected at the multicritical transition. We also perform a five-loop field-theoretical analysis of the renormalization-group flow. It shows that bicritical systems are not in the attraction domain of the stable decoupled fixed point. Thus, in these systems--high-Tc cuprates should belong to this class--the multicritical point corresponds to a first-order transition.Comment: 18 page

Critical X-ray Scattering Studies of Jahn-Teller Phase Transitions in TbV1−x_{1-x}Asx_{x}O4_{4}

The critical behaviour associated with cooperative Jahn-Teller phase transitions in TbV$_{1-x}$As$_{x}$O$_{4}$ (where \textit{x} = 0, 0.17, 1) single crystals have been studied using high resolution x-ray scattering. These materials undergo continuous tetragonal $\to$ orthorhombic structural phase transitions driven by Jahn-Teller physics at T$_C$ = 33.26(2) K, 30.32(2) K and 27.30(2) K for \textit{x} = 0, 0.17 and 1 respectively. The orthorhombic strain was measured close to the phase transition and is shown to display mean field behavior in all three samples. Pronounced fluctuation effects are manifest in the longitudinal width of the Bragg scattering, which diverges as a power law, with an exponent given by $x=0.45 \pm 0.04$, on approaching the transition from either above or below. All samples exhibited twinning; however the disordered x = 0.17 sample showed a broad distribution of twins which were stable to relatively low temperatures, well below T$_C$. This indicates that while the orthorhombic strain continues to develop in a conventional mean field manner in the presence of disorder, twin domains are easily pinned by the quenched impurities and their associated random strains.Comment: 8 pages, 6 figure