Aging in ferromagnetic systems at criticality near four dimensions

Universal equilibrium scaling functions at short times after a quench

By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.

Nonequilibrium fluctuation-dissipation relations of interacting Brownian particles driven by shear

We present a detailed analysis of the fluctuation-dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the many-particle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium FDT. An asymptotically constant relation connects response and fluctuations during the shear driven decay, restoring the form of the FDT with, however, a ratio different from the equilibrium one. At short times, the equilibrium FDT holds. We follow two independent approaches whose results are in qualitative agreement. To discuss the derived fluctuation-dissipation ratios, we show an exact reformulation of the susceptibility which contains not the full Smoluchowski operator as in equilibrium, but only its well defined Hermitian part. This Hermitian part can be interpreted as governing the dynamics in the frame comoving with the probability current. We present a simple toy model which illustrates the FDT violation in the sheared colloidal system.

Test of local scale invariance from the direct measurement of the response function in the Ising model quenched to and below T(C)

In order to check on a recent suggestion that local scale invariance [M. Henkel, Phys. Rev. Lett. 87, 265701 (2001)] might hold when the dynamics is of Gaussian nature, we have carried out the measurement of the response function in the kinetic Ising model with Glauber dynamics quenched to T(C) in d=4, where Gaussian behavior is expected to apply, and in the two other cases of the d=2 model quenched to T(C) and to below T(C), where instead deviations from Gaussian behavior are expected to appear. We find that in the d=4 case there is an excellent agreement between the numerical data, the local scale invariance prediction and the analytical Gaussian approximation. No logarithmic corrections are numerically detected. Conversely, in the d=2 cases, both in the quench to T(C) and to below T(C), sizable deviations of the local scale invariance behavior from the numerical data are observed. These results do support the idea that local scale invariance might miss to capture the non-Gaussian features of the dynamics. The considerable precision needed for the comparison has been achieved through the use of a fast new algorithm for the measurement of the response function without applying the external field. From these high quality data we obtain a=0.27+/-0.002 for the scaling exponent of the response function in the d=2 Ising model quenched to below T(C), in agreement with previous results.

Universality of fluctuation-dissipation ratios: the ferromagnetic model

We calculate analytically the fluctuation-dissipation ratio (FDR) for Ising ferromagnets quenched to criticality, both for the long-range model and its short-range analog in the limit of large dimension. Our exact solution shows that, for both models, if the system is unmagnetized while if the initial magnetization is nonzero. This indicates that two different classes of critical coarsening dynamics need to be distinguished depending on the initial conditions, each with its own nontrivial FDR. We also analyze the dependence of the FDR on whether local and global observables are used. These results clarify how a proper local FDR (and the corresponding effective temperature) should be defined in long-range models in order to avoid spurious inconsistencies and maintain the expected correspondence between local and global results; global observables turn out to be far more robust tools for detecting nonequilibrium FDRs.

Universal aging properties at a disordered critical point

We investigate, analytically near the dimension d(uc) =4 and numerically in d=3 , the nonequilibrium relaxational dynamics of the randomly diluted Ising model at criticality. Using the exact renormalization-group method to one loop, we compute the two times t, t(w) correlation function and fluctuation dissipation ratio (FDR) for any Fourier mode of the order parameter, of finite wave vector q . In the large time separation limit, the FDR is found to reach a nontrivial value X(infinity) independently of (small) q and coincide with the FDR associated to the total magnetization obtained previously. Explicit calculations in real space show that the FDR associated to the local magnetization converges, in the asymptotic limit, to this same value X(infinity). Through a Monte Carlo simulation, we compute the autocorrelation function in three dimensions, for different values of the dilution fraction p at T(c) (p) . Taking properly into account the corrections to scaling, we find, according to the renormalization-group predictions, that the autocorrelation exponent lambda(c) is independent of p . The analysis is complemented by a study of the nonequilibrium critical dynamics following a quench from a completely ordered state.

Aging in the glass phase of a two-dimensional random periodic elastic system

Using the renormalization group method we investigate the nonequilibrium relaxation of the (Cardy-Ostlund) 2D random sine-Gordon model, which describes pinned arrays of lines. Its statics exhibit a marginal (theta = 0) glass phase for T < Tg described by a line of fixed points. We obtain the universal scaling functions for two-time dynamical response and correlations near Tg for various initial conditions, as well as the autocorrelation exponent. The fluctuation dissipation ratio is found to be nontrivial and continuously dependent on T.

Limits and regulations for mycotoxins in food and feed

Mycotoxins are natural contaminants whose presence in food- and feedstuffs cannot be completely avoided. Since several mycotoxins have been associated with and implicated in human and animal diseases there is a need to establish maximum levels, guidelines or action levels for them in some kinds of commodities. International and government authorities in many countries have been investing in mycotoxins research and initiating administrative actions for elaboration of legislation and implementing regulatory measures for the control of mycotoxins. Codex Alimentarius Commission is established international legislation on food and feed. In European Union specific limits and regulations for mycotoxins and other contaminants are constructed under the general Codex standards and based on proposal from European Commission. The legal basis for European Commission became available with the framework Council Regulation (EEC) No 315/93. In this paper, legislation regarding maximum levels for certain mycotoxins in food- and feedstuffs in European Community and other countries were reviewed and discussed.

Nominal thermodynamic temperature in nonequilibrium kinetic Ising models

We show that a nominal temperature can be consistently and uniquely defined everywhere in the phase diagram of large classes of nonequilibrium kinetic Ising spin models. In addition, we confirm that, at critical points, the large-time "fluctuation-dissipation ratio" X( infinity ) is a universal amplitude ratio, and find in particular X( infinity ) approximately 0.33(1) and X( infinity )=1 / 2 for the magnetization in, respectively, the two-dimensional Ising and voter universality classes.

Exact multilocal renormalization of the effective action: application to the random sine Gordon model statics and nonequilibrium dynamics

We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal parts yields a closed exact RG equation for the local part, to a given order in the local part. The method is illustrated on the O(N) model by straightforwardly recovering the eta exponent and scaling functions. Then it is applied to study the glass phase of the Cardy-Ostlund, random phase sine Gordon model near the glass transition temperature. The static correlations and equilibrium dynamical exponent z are recovered and several results are obtained, such as the equilibrium two-point scaling functions. The nonequilibrium, finite momentum, two-time t,t' response and correlations are computed. They are shown to exhibit scaling forms, characterized by exponents lambda(R) not equal lambda(C), as well as universal scaling functions that we compute. The fluctuation dissipation ratio is found to be nontrivial and of the form X[q(z)(t-t'),t/t']. Analogies and differences with pure critical models are discussed.

Dynamic structure factor of the three-dimensional Ising model with purely relaxational dynamics

We compute the dynamic structure factor for the three-dimensional Ising model with a purely relaxational dynamics (model A). We perform a perturbative calculation in the epsilon expansion, at two loops in the high-temperature phase and at one loop in the temperature magnetic-field plane, and a Monte Carlo simulation in the high-temperature phase. We find that the dynamic structure factor is very well approximated by its mean-field Gaussian form up to moderately large values of frequency omega and momentum k. In the region we can investigate, k(xi) less than or equal 5, omega(tau) less than or equal 10, where xi is the correlation length and tau is the zero-momentum autocorrelation time, deviations are at most of a few percent.

Aging at criticality in model-C dynamics

We study the off-equilibrium two-point critical response and correlation functions for the relaxational dynamics with a coupling to a conserved density (model C) of the O(N) vector model. They are determined in an epsilon=4-d expansion for vanishing momentum. We briefly discuss their scaling behaviors and the associated scaling forms are determined up to first order in epsilon. The corresponding fluctuation-dissipation ratio has a nontrivial large time limit in the aging regime and, up to one-loop order, it is the same as that of the model A for the physically relevant case N=1. The comparison with predictions of local scale invariance is also discussed.

Two-loop critical fluctuation-dissipation ratio for the relaxational dynamics of the O(N) Landau-Ginzburg Hamiltonian

The off-equilibrium purely dissipative dynamics (model A) of the O(N) vector model is considered at criticality in an epsilon=4-d>0 expansion up to O(epsilon(2)). The scaling behavior of two-time response and correlation functions at zero momentum, the associated universal scaling functions and the nontrivial limit of the fluctuation-dissipation ratio are determined in the aging regime.