Modified Scaling Relation for the Random-Field Ising Model

We investigate the low-temperature critical behavior of the three dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature $T \to 0$ the usual scaling relations have to be modified as far as the exponent $\alpha$ of the specific heat is concerned. At zero temperature, the Rushbrooke equation is modified to $\alpha + 2 \beta + \gamma = 1$, an equation which we expect to be valid also for other systems with similar critical behavior. We test the scaling theory numerically for the three dimensional random field Ising system with Gaussian probability distribution of the random fields by a combination of calculations of exact ground states with an integer optimization algorithm and Monte Carlo methods. By a finite size scaling analysis we calculate the critical exponents $\nu \approx 1.0$, $\beta \approx 0.05$, $\bar{\gamma} \approx 2.9$ $\gamma \approx 1.5$ and $\alpha \approx -0.55$.Comment: 4 pages, Latex, Postscript Figures include

New algorithm and results for the three-dimensional random field Ising Model

The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges 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 sytems 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.Comment: 24 pages, 23 figure

Electrophysical methods of separation of metal cations in the moving salts solution

The results of experiments on the excitation of the phenomenon of selective drift of solvated ions under the influence of an external "asymmetric" electric field to the circulating solution of calcium chloride and magnesium salts in a polar liquid dielectric - water are shown. The purpose of the experiments was to determine the influence of the field frequency and amplitude of the field strength on the excitation phenomenon, and the study of the operating characteristics of the testing apparatus - a dividing cell. The dependences of the separation efficiency of solvated cations from the frequency of the external field and the excitation threshold of the phenomenon from the field strength in the separation cell are defined

Monte Carlo study of the random-field Ising model

Using a cluster-flipping Monte Carlo algorithm combined with a generalization of the histogram reweighting scheme of Ferrenberg and Swendsen, we have studied the equilibrium properties of the thermal random-field Ising model on a cubic lattice in three dimensions. We have equilibrated systems of LxLxL spins, with values of L up to 32, and for these systems the cluster-flipping method appears to a large extent to overcome the slow equilibration seen in single-spin-flip methods. From the results of our simulations we have extracted values for the critical exponents and the critical temperature and randomness of the model by finite size scaling. For the exponents we find nu = 1.02 +/- 0.06, beta = 0.06 +/- 0.07, gamma = 1.9 +/- 0.2, and gammabar = 2.9 +/- 0.2.Comment: 12 pages, 6 figures, self-expanding uuencoded compressed PostScript fil

Critical Exponents of the pure and random-field Ising models

We show that current estimates of the critical exponents of the three-dimensional random-field Ising model are in agreement with the exponents of the pure Ising system in dimension 3 - theta where theta is the exponent that governs the hyperscaling violation in the random case.Comment: 9 pages, 4 encapsulated Postscript figures, REVTeX 3.

Ground state numerical study of the three-dimensional random field Ising model

The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 60^3. For each realization of the normalized random fields, the strength of the random field, Delta and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the H-Delta plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.Comment: 10 pages, 6 figures; new references and small changes to tex

Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?

In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the random fields it is found that the correlation length $\xi$ diverges with an exponent $\nu=1.1\pm0.2$ at the critical temperature and that $\chi\sim\xi^{2-\eta}$ with $\eta=0.50\pm0.05$ for the connected susceptibility and $\chi_{\rm dis}\sim\xi^{4-\bar{\eta}}$ with $\bar{\eta}=1.03\pm0.05$ for the disconnected susceptibility. Together with the amplitude ratio $A=\lim_{T\to T_c}\chi_{\rm dis}/\chi^2(h_r/T)^2$ being close to one this gives further support for a two exponent scaling scenario implying $\bar{\eta}=2\eta$. The magnetization behaves discontinuously at the transition, i.e. $\beta=0$, indicating a first order transition. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multi-peak structure that is characteristic for the phase-coexistence at first order phase transition points.Comment: 14 pages, RevTeX, 11 postscript figures (fig9.ps and fig11.ps should be printed separately

Critical behavior of a fluid in a disordered porous matrix: An Ornstein-Zernike approach

Using a liquid-state approach based on Ornstein-Zernike equations, we study the behavior of a fluid inside a porous disordered matrix near the liquid-gas critical point.The results obtained within various standard approximation schemes such as lowest-order $\gamma$-ordering and the mean-spherical approximation suggest that the critical behavior is closely related to that of the random-field Ising model (RFIM).Comment: 10 pages, revtex, to appear in Physical Review Letter

Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations

Exact ground states of three-dimensional random field Ising magnets (RFIM) with Gaussian distribution of the disorder are calculated using graph-theoretical algorithms. Systems for different strengths h of the random fields and sizes up to N=96^3 are considered. By numerically differentiating the bond-energy with respect to h a specific-heat like quantity is obtained, which does not appear to diverge at the critical point but rather exhibits a cusp. We also consider the effect of a small uniform magnetic field, which allows us to calculate the T=0 susceptibility. From a finite-size scaling analysis, we obtain the critical exponents \nu=1.32(7), \alpha=-0.63(7), \eta=0.50(3) and find that the critical strength of the random field is h_c=2.28(1). We discuss the significance of the result that \alpha appears to be strongly negative.Comment: 9 pages, 9 figures, 1 table, revtex revised version, slightly extende