Quasicritical behavior and first-order transition in the d=3 random-field Ising model

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.

Neutron Scattering Measurements of the Staggered Magnetization of an Antiferromagnetic Epitaxial thin Film FeF2

Elastic neutron scattering measurements performed at the NIST reactor have been used to measure the staggered magnetization near the transition temperature in a thin antiferromagnetic epitaxial film of FeF2 of thickness 0.8μm and diameter 1cm grown on a diamagnetic (001) ZnF2substrate by MBE. The use of a thin film permits extinction-free Bragg intensities, something which has proven impossible in bulk crystals. The growth techniques yield sufficient crystal quality to observed resolution limited Magnetic Bragg scattering peaks and to approach the transition within a reduced temperature of |t| = 0.003. The structure quality of this sample has been characterized using X-ray double crystal diffraction with a measured rocking curve lin ewidth of less than 30 arc sec. The sample thickness, while small enough to eliminate extinction, is sufficiently large to assure three-dimensional Ising Model critical behavior. We indeed observe critical behavior consistent with theoretical predictions. The success of the thin film experiments demonstrates the possibilities of extinction-free Bragg scattering measurements in a variety of antiferromagnetic Materials, including multilayered systems.

Phase transitions in a three-dimensional kinetic spin-1/2 Ising model with random field: effective-field-theory study

The dynamical phase transitions of the kinetic Ising model in the presence of a random magnetic field with a bimodal probability distribution is studied by using effective-field theory (EFT) with correlations. We have used a Glauber-type stochastic dynamic to describe the time evolution of the system, where the system strongly depends on the H≡√<H(i)(2)>(c) root mean square deviation of the magnetic field. The EFT dynamic equation is given for the simple cubic lattice (z=6), and the dynamic order parameter is calculated. The system presents ferromagnetic and paramagnetic states for low and high temperatures, respectively. Our results predict first-order transitions at low temperatures and large disorder strengths, which corresponds to the existence of a nonequilibrium tricritical point (TCP) in a phase diagram in the T-H plane. We compare the results with the equilibrium phase diagram, where only the first-order line is different. Our qualitative results are compatible with recent Monte Carlo simulations.

Finite-size scaling in Ising-like systems with quenched random fields: evidence of hyperscaling violation

In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced with a modified hyperscaling relation. As a result, standard formulations of finite-size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free-energy cost ΔF of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, ΔF∝L(θ), with θ as the violation of hyperscaling critical exponent and L as the linear extension of the system. This modified behavior facilitates a number of numerical approaches that can be used to locate critical points in random field systems from finite-size simulation data. We test and confirm the approaches on two random field systems in three dimensions, namely, the random field Ising model and the demixing transition in the Widom-Rowlinson fluid with quenched obstacles.

Lack of self-averaging of the specific heat in the three-dimensional random-field Ising model

We apply the recently developed critical minimum-energy subspace scheme for the investigation of the random-field Ising model. We point out that this method is well suited for the study of this model. The density of states is obtained via the Wang-Landau and broad histogram methods in a unified implementation by employing the N-fold version of the Wang-Landau scheme. The random fields are obtained from a bimodal distribution (hi = +/-2), and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from L=4 to L=32. Observing the finite-size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat. The lack of self-averaging of this quantity is fully illustrated, and it is shown that this property may be related to the question mentioned above.

Replica-exchange algorithm and results for the three-dimensional random field ising model

The random field Ising model with Gaussian disorder is studied using a different Monte Carlo algorithm. The algorithm combines the advantages of the replica-exchange method and the two-replica cluster method and is much more efficient than the Metropolis algorithm for some disorder realizations. Three-dimensional systems of size 24(3) are studied. Each realization of disorder is simulated at a value of temperature and uniform field that is adjusted to the phase-transition region for that disorder realization. Energy and magnetization distributions show large variations from one realization of disorder to another. For some realizations of disorder there are three well separated peaks in the magnetization distribution and two well separated peaks in the energy distribution suggesting a first-order transition.