Order parameter criticality of the d = 3 random-field Ising antiferromagnet Fe0.85Zn0.15F2

Random-field Ising model on isometric lattices: Ground states and non-Porod scattering

We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δ_{c} at zero temperature with high accuracy. For the SC lattice, our estimate (Δ_{c}=2.278±0.002) is consistent with earlier reports. For the BCC and FCC lattices, Δ_{c}=3.316±0.002 and 5.160±0.002, respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α=0.5±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy E_{i}(L) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.

Phase diagram of a three-dimensional antiferromagnet with random magnetic anisotropy

Three-dimensional antiferromagnets with random magnetic anisotropy (RMA) that have been experimentally studied to date have competing two-dimensional and three-dimensional exchange interactions which can obscure the authentic effects of RMA. The magnetic phase diagram of Fe_{x}Ni_{1-x}F_{2} epitaxial thin films with true random single-ion anisotropy was deduced from magnetometry and neutron scattering measurements and analyzed using mean-field theory. Regions with uniaxial, oblique, and easy-plane anisotropies were identified. A RMA-induced glass region was discovered where a Griffiths-like breakdown of long-range spin order occurs.

Two-dimensional Ising model criticality in a three-dimensional uniaxial relaxor ferroelectric with frozen polar nanoregions

The charge-disordered three-dimensional uniaxial relaxor ferroelectric Sr0.61Ba0.39Nb2O6 splits up into metastable polar nanoregions and paraelectric interfaces upon cooling from above Tc. The frozen polar nanoregions are verified by piezoresponse force microscopy, respond domainlike to dynamic light scattering and dielectric excitation, reveal nonergodicity at T>Tc via global aging, and coalesce into polar nanodomains below Tc. Contrastingly, the percolating system of unperturbed interfaces becomes ferroelectric with two-dimensional Ising-model-like critical exponents alpha=0, beta=1/8, and gamma=7/4, as corroborated by ac calorimetry, second harmonic generation, and susceptometry, respectively.

Instanton analysis of hysteresis in the three-dimensional random-field Ising model

We study the magnetic hysteresis in the random-field Ising model in 3D. We discuss the disorder dependence of the coercive field Hc, and obtain an analytical description of the smooth part of the hysteresis below and above Hc, by identifying the disorder configurations (instantons) that are the most probable to trigger local avalanches. We estimate the critical disorder strength at which the hysteresis curve becomes continuous. From an instanton analysis at zero field we obtain a description of local two-level systems in the ferromagnetic phase.

Phase transitions in a disordered system in and out of equilibrium

The equilibrium and nonequilibrium disorder-induced phase transitions are compared in the random-field Ising model. We identify in the demagnetized state the correct nonequilibrium hysteretic counterpart of the T=0 ground state, and present evidence of universality. Numerical simulations in d=3 indicate that exponents and scaling functions coincide, while the location of the critical point differs, as corroborated by exact results for the Bethe lattice. These results are of relevance for optimization, and for the generic question of universality in the presence of disorder.

Change from 3D-Ising to random field-Ising-model criticality in a uniaxial relaxor ferroelectric

Pyroelectric measurements of polarization have been used to determine the temperature dependence of the polarization in strontium barium niobate, SBN:Ce, close to its phase transition temperature T(c) approximately 317 K. A gradual increase of the critical exponent from beta approximately 0.13 to beta approximately 0.30 is observed when decreasing the initial polarization from 100% to 0.8% of the saturation value. A change from three-dimensional random-field Ising to pure Ising model behavior is conjectured and explained by a gradual compensation of quenched random electric fields by those emerging from charged fractal nanodomain walls.

Microscopic description of an Ising spin glass near the percolation threshold

Monte Carlo results using a microscopic model to describe FexZn(1-x)F2 indicate that its spin-glass phase at x=0.25 and zero magnetic field is characterized by the presence of antiferromagnetic fractal domains, separated by random vacancies and strongly correlated in time. The effective local random-field distribution corroborates this glassy behavior, which emerges irrespective of ab initio competing interactions and is a consequence of the fractal domain structure near the percolation threshold, x(p)=0.24. The aging properties of the system are in agreement with predictions of short-range stochastic spin-glass models and with the droplets model for spin glass close to percolation.