Critical Behavior of the Random-Field Ising Model

We study the critical properties of the random field Ising model in general dimension d using high-temperature expansions for the susceptibility, χ=∑j[〈σiσj⟩T-〈σi⟩T〈σj⟩T]h and the structure factor, G=∑j[〈σiσj⟩T]h, where 〈⟩T indicates a canonical average at temperature T for an arbitrary configuration of random fields and [ ]h indicates an average over random fields. We treated two distributions of random fields, the bimodal in which each hi=±h0 and a Gaussian distribution in which each hi has variance h02. We obtained series for χ and G in the form ∑n=1,15an(g,d)(J/T)n, where J is the exchange constant and the coefficients an(g,d) are polynomials in g≡h02/J2 and in d. We assume that as T approaches its critical value, Tc, one has χ~(T-Tc)−γ and G~(T-Tc)−γ. For dimensions above d=2 we find a range of values of g for which the critical exponents obtained from our series seem not to depend on g. For large values of g our results show a g dependence which is attributable to either a tricritical point or a first-order transition. All our results for critical exponents suggest that γ¯=2γ, in agreement with the two-exponent scaling picture. In addition we have also constructed series for the amplitude ratio, A=(G/χ2)(T2)/(gJ2). We find that A approaches a constant value as T→Tc (consistent with γ¯=2γ) with A~1. It appears that A is somewhat larger for the bimodal than for the Gaussian model, in agreement with a recent analysis at high d

Evidence for Two Exponent Scaling in the Random Field Ising Model

Novel methods were used to generate and analyze new 15 term high temperature series for both the (connected) susceptibility χ and the structure factor (disconnected susceptibility) χd for the random field Ising model with dimensionless coupling K=J/kT, in general dimension d. For both the bimodal and the Gaussian field distributions, with mean square field J2g, we find that (χd-χ)/K2gχ2=1 as T→Tc(g), for a range of [h2]=J2g and d=3,4,5. This confirms the exponent relation γ¯=2γ (where χd~t−γ¯, χ~t−γ, t=T-Tc) providing that random field exponents are determined by two (and not three) independent exponents. We also present new accurate values for γ

Intentional Forgetting: Current Status and Future Prospects of Research

Background. Classical psychology has considered forgetting as a negative process of failure of memorization and extraction, but did not deem it a separate mental process with specific features. The pioneer studies of intentional forgetting were conducted only in the late 1960s. Therefore, it seems to us relevant to present an analysis of the research methods that have been used to study purposeful forgetting. The Objective is to analyze thoroughly intentional forgetting in modern cognitive psychology and to justify the assumption that the productive development of intentional forgetting issues should be associated with the priority attention to the regulating function of the mnemonic goal and its structure. A hypothesis lies in the fact that a particular operation of the mnemonic action of forgetting consists in disconnecting the content links between the constituent mnemonic elements made during memorizing process. Design. Two of the most common experimental procedures for inducing the effect of reducing the reproduction of stimulus material after the «Forget» instruction are described: the item method and the list method. The results show four ways of interpreting the intentional forgetting effect: the aspirations of the subjects to meet the experimenter’s expectations, selective encoding and selective processing of the material presented, the mechanism of active «retrieval inhibition» and eliminating the mnemonic trace. The concept of mnemonic action introduced in the works of P.I. Zinchenko and the concept of the mnemonic scheme as a program for the subsequent reproduction of V.Ya. Lyaudis are considered. The Research Results suggest that when trying to perform an inadequate mnemonic query, the subject is forced to implement an additional operation, which may be attributed to potential forgetting operations. The development of this hypothesis consists in the theoretical description of operations that destroy the existing mnemonic scheme, followed by an empirical test of their amnesogenic effectiveness. Such an approach can be used in further studies of intentional forgetting. Conclusion. Encoding and processing of mnemonic material, extraction, and the mechanism for inhibited reproduction play a role in shaping the effect of intentional forgetting. Considering the fact that the mnemonic trace can fade over time or for other reasons, forgetting is deemed as a multifaceted process. Prospects for the development of this subject area should be conducted using the mnemonic construct

Measuring sensory and marketing influences on consumers' choices among food and beverage product brands

Advance in food science depends on measuring the factors in human perception that influence eaters' activities with branded products. Assessed samples must include at least two levels of a sensed material characteristic (e.g. sucrose) or conceptual marketing attribute (e.g. “low fat”), minimally confounded by other features. Each feature needs to be measured for its effect on the individual's objective achievement of choosing among the samples for a familiar context of use. These influences interact, consciously and unconsciously. This theory of how a mind works has generated a wide range of scientifically illuminating and commercially practical examples, illustrated in this review

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

Test of Universality in the Ising Spin Glass Using High Temperature Graph Expansion

We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility \chi_EA are obtained to order 13 in the expansion variable (J/(k_B T))^2 for the general d-dimensional hyper-cubic lattice, where the parameter J determines the width of the distributions. We explain in detail how the expansions are calculated. The analysis, using the Dlog-Pad\'e approximation and the techniques known as M1 and M2, leads to estimates for the critical threshold (J/(k_B T_c))^2 and for the critical exponent \gamma in dimensions 4, 5, 7 and 8 for all the distribution functions. In each dimension the values for \gamma agree, within their uncertainty margins, with a common value for the different distributions, thus confirming universality.Comment: 13 figure

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

Full reduction of large finite random Ising systems by RSRG

We describe how to evaluate approximately various physical interesting quantities in random Ising systems by direct renormalization of a finite system. The renormalization procedure is used to reduce the number of degrees of freedom to a number that is small enough, enabling direct summing over the surviving spins. This procedure can be used to obtain averages of functions of the surviving spins. We show how to evaluate averages that involve spins that do not survive the renormalization procedure. We show, for the random field Ising model, how to obtain the "connected" 2-spin correlation function and the "disconnected" 2-spin correlation function. Consequently, we show how to obtain the average susceptibility and the average energy. For an Ising system with random bonds and random fields we show how to obtain the average specific heat. We conclude by presenting our numerical results for the average susceptibility and the "connected" 2-spin correlation function along one of the principal axes. (We believe this to be the first time, where the full three dimensional correlation is calculated and not just parameters like Nu or Eta.) The results for the average susceptibility are used to extract the critical temperature and critical exponents of the 3D random field Ising system.Comment: 30 pages, 17 figure

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.