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

Non Markovian persistence in the diluted Ising model at criticality

We investigate global persistence properties for the non-equilibrium critical dynamics of the randomly diluted Ising model. The disorder averaged persistence probability $\bar{{P}_c}(t)$ of the global magnetization is found to decay algebraically with an exponent $\theta_c$ that we compute analytically in a dimensional expansion in $d=4-\epsilon$. Corrections to Markov process are found to occur already at one loop order and $\theta_c$ is thus a novel exponent characterizing this disordered critical point. Our result is thoroughly compared with Monte Carlo simulations in $d=3$, which also include a measurement of the initial slip exponent. Taking carefully into account corrections to scaling, $\theta_c$ is found to be a universal exponent, independent of the dilution factor $p$ along the critical line at $T_c(p)$, and in good agreement with our one loop calculation.Comment: 7 pages, 4 figure

Letting the Right Ones In: Whitelists, Jurisdictional Reputation, and the Racial Dynamics of Online Gambling Regulation.

Using a case study of a recent UK whitelist intended to regulate online gambling, I examine the affective politics of listing. I pay particular attention to the racial dynamics of black and white listing. By charting how the gambling whitelist worked and failed to work as a tool in the designation of jurisdictional reputation, I argue that the use and subsequent abandonment of the whitelist shows the centrality of racial dynamics to listing practices, particularly in relation to how the list was deployed in debates about the trustworthiness of the Kahnawá:ke territory and Antigua and Barbuda. In section 5 I examine what happened after the demise of the online gambling whitelist. Although non-listing techniques of governance look to be expanding, in the form of increased surveillance of individual gamblers, lists continue to play a key role in the UK government’s new model of gambling regulation. I suggest that this confirms the co-constitutive and mutually reinforcing nature of black and white lists as techniques of governance, and the value of exploring them and their racialized implications together

Computer simulation of the critical behavior of 3D disordered Ising model

The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.Comment: 14 RevTeX pages, 6 figure

Real-space renormalization group for the random-field Ising model

We present real--space renormalization group (RG) calculations of the critical properties of the random--field Ising model on a cubic lattice in three dimensions. We calculate the RG flows in a two--parameter truncation of the Hamiltonian space. As predicted, the transition at finite randomness is controlled by a zero temperature, disordered critical fixed point, and we exhibit the universal crossover trajectory from the pure Ising critical point. We extract scaling fields and critical exponents, and study the distribution of barrier heights between states as a function of length scale.Comment: 12 pages, CU-MSC-757

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

Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus ϵ1/2\epsilon^{1/2}-Expansion

We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in a replica limit n=0 5-loop renormalization group functions of the $\phi^4$-theory with O(n)-symmetric and cubic interactions (H.Kleinert and V.Schulte-Frohlinde, Phys.Lett. B342, 284 (1995)). The minimal subtraction scheme allows to develop either the $\epsilon^{1/2}$-expansion series or to proceed in the 3d approach, performing expansions in terms of renormalized couplings. Doing so, we compare both perturbation approaches and discuss their convergence and possible Borel summability. To study the crossover effect we calculate the effective critical exponents providing a local measure for the degree of singularity of different physical quantities in the critical region. We report resummed numerical values for the effective and asymptotic critical exponents. Obtained within the 3d approach results agree pretty well with recent Monte Carlo simulations. $\epsilon^{1/2}$-expansion does not allow reliable estimates for d=3.Comment: 35 pages, Latex, 9 eps-figures included. The reference list is refreshed and typos are corrected in the 2nd versio

Monte Carlo Simulation of a Random-Field Ising Antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.Comment: 10 pages, 11 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

Correlation functions in the two-dimensional random-field Ising model

Transfer-matrix methods are used to study the probability distributions of spin-spin correlation functions $G$ in the two-dimensional random-field Ising model, on long strips of width $L = 3 - 15$ sites, for binary field distributions at generic distance $R$, temperature $T$ and field intensity $h_0$. For moderately high $T$, and $h_0$ of the order of magnitude used in most experiments, the distributions are singly-peaked, though rather asymmetric. For low temperatures the single-peaked shape deteriorates, crossing over towards a double-$\delta$ ground-state structure. A connection is obtained between the probability distribution for correlation functions and the underlying distribution of accumulated field fluctuations. Analytical expressions are in good agreement with numerical results for $R/L \gtrsim 1$, low $T$, $h_0$ not too small, and near G=1. From a finite-size {\it ansatz} at $T=T_c (h_0=0)$, $h_0 \to 0$, averaged correlation functions are predicted to scale with $L^y h_0$, $y =7/8$. From numerical data we estimate y=0.875 \pm 0.025$, in excellent agreement with theory. In the same region, the RMS relative width$W$of the probability distributions varies for fixed$R/L=1$as$W \sim h_0^{\kappa} f(L h_0^u)$with$\kappa \simeq 0.45$,$u \simeq 0.8$;$f(x)$appears to saturate when$x \to \infty$, thus implying$W \sim h_0^{\kappa}$in$d=2$.Comment: RevTeX code for 8 pages, 7 eps figures, to appear in Physical Review E (1999