Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG

Non-equilibrium dynamics of classical random Ising spin chains are studied using asymptotically exact real space renormalization group. Specifically the random field Ising model with and without an applied field (and the Ising spin glass (SG) in a field), in the universal regime of a large Imry Ma length so that coarsening of domains after a quench occurs over large scales. Two types of domain walls diffuse in opposite Sinai random potentials and mutually annihilate. The domain walls converge rapidly to a set of system-specific time-dependent positions {\it independent of the initial conditions}. We obtain the time dependent energy, magnetization and domain size distribution (statistically independent). The equilibrium limits agree with known exact results. We obtain exact scaling forms for two-point equal time correlation and two-time autocorrelations. We also compute the persistence properties of a single spin, of local magnetization, and of domains. The analogous quantities for the spin glass are obtained. We compute the two-point two-time correlation which can be measured by experiments on spin-glass like systems. Thermal fluctuations are found to be dominated by rare events; all moments of truncated correlations are computed. The response to a small field applied after waiting time $t_w$, as measured in aging experiments, and the fluctuation-dissipation ratio $X(t,t_w)$ are computed. For $(t-t_w) \sim t_w^{\hat{\alpha}}$, $\hat{\alpha} <1$, it equals its equilibrium value X=1, though time translational invariance fails. It exhibits for $t-t_w \sim t_w$ aging regime with non-trivial $X=X(t/t_w) \neq 1$, different from mean field.Comment: 55 pages, 9 figures, revte

Ultrametricity in 3D Edwards-Anderson spin glasses

We perform an accurate test of Ultrametricity in the aging dynamics of the three dimensional Edwards-Anderson spin glass. Our method consists in considering the evolution in parallel of two identical systems constrained to have fixed overlap. This turns out to be a particularly efficient way to study the geometrical relations between configurations at distant large times. Our findings strongly hint towards dynamical ultrametricity in spin glasses, while this is absent in simpler aging systems with domain growth dynamics. A recently developed theory of linear response in glassy systems allows to infer that dynamical ultrametricity implies the same property at the level of equilibrium states.Comment: 4 pages, 5 figure

Aging dynamics of heterogeneous spin models

We investigate numerically the dynamics of three different spin models in the aging regime. Each of these models is meant to be representative of a distinct class of aging behavior: coarsening systems, discontinuous spin glasses, and continuous spin glasses. In order to study dynamic heterogeneities induced by quenched disorder, we consider single-spin observables for a given disorder realization. In some simple cases we are able to provide analytical predictions for single-spin response and correlation functions. The results strongly depend upon the model considered. It turns out that, by comparing the slow evolution of a few different degrees of freedom, one can distinguish between different dynamic classes. As a conclusion we present the general properties which can be induced from our results, and discuss their relation with thermometric arguments.Comment: 39 pages, 36 figure

Extended droplet theory for aging in short-ranged spin glasses and a numerical examination

We analyze isothermal aging of a four dimensional Edwards-Anderson model in detail by Monte Carlo simulations. We analyze the data in the view of an extended version of the droplet theory proposed recently (cond-mat/0202110) which is based on the original droplet theory plus conjectures on the anomalously soft droplets in the presence of domain walls. We found that the scaling laws including some fundamental predictions of the original droplet theory explain well our results. The results of our simulation strongly suggest the separation of the breaking of the time translational invariance and the fluctuation dissipation theorem in agreement with our scenario.Comment: 27 pages, 39 epsfiles, revised versio

Scaling properties in off equilibrium dynamical processes

In the present paper, we analyze the consequences of scaling hypotheses on dynamic functions, as two times correlations $C(t,t')$. We show, under general conditions, that $C(t,t')$ must obey the following scaling behavior $C(t,t') = \phi_1(t)^{f(\beta)}{\cal{S}}(\beta)$, where the scaling variable is $\beta=\beta(\phi_1(t')/\phi_1(t))$ and $\phi_1(t')$, $\phi_1(t)$ two undetermined functions. The presence of a non constant exponent $f(\beta)$ signals the appearance of multiscaling properties in the dynamics.Comment: 6 pages, no figure

Associations among neighborhood poverty, perceived neighborhood environment, and depressed mood are mediated by physical activity, perceived individual control, and loneliness

Few studies have documented the pathways through which individual level variables mediate the effects of neighborhoods on health. This study used structural equation modeling to examine if neighborhood characteristics are associated with depressive symptoms, and if so, what factors mediated these relationships. Cross-sectional data came from a sample of mostly rural, older adults in North Carolina (n = 1,558). Mediation analysis indicated that associations among neighborhood characteristics and depressive symptoms were mediated by loneliness (standardized indirect effect = −0.19, p < 0.001), physical activity (standardized indirect effect = −0.01, p = 0.003), and perceived individual control (standardized indirect effect = −0.07, p = 0.02) with loneliness emerging as the strongest mediator. Monitoring such individual mediators in formative and process evaluations may increase the precision of neighborhood-based interventions and policies

Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit

We study the dynamics of the one dimensional disordered trap model presenting a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an external force is applied from the very beginning at $t=0$, or only after a waiting time $t_w$, in the linear as well as in the non-linear response regime. Using a real-space renormalization procedure that becomes exact in the limit of strong disorder $\mu \to 0$, we obtain explicit results for many observables, such as the diffusion front, the mean position, the thermal width, the localization parameters and the two-particle correlation function. In particular, the scaling functions for these observables give access to the complete interpolation between the unbiased case and the directed case. Finally, we discuss in details the various regimes that exist for the averaged position in terms of the two times and the external field.Comment: 27 pages, 1 eps figur

From Linear to Nonlinear Response in Spin Glasses: Importance of Mean-Field-Theory Predictions

Deviations from spin-glass linear response in a single crystal Cu:Mn 1.5 at % are studied for a wide range of changes in magnetic field, $\Delta H$. Three quantities, the difference $TRM-(MFC-ZFC)$, the effective waiting time, $t_{w}^{eff}$, and the difference $TRM(t_{w})-TRM(t_{w}=0)$ are examined in our analysis. Three regimes of spin-glass behavior are observed as $\Delta H$ increases. Lines in the $(T,\Delta H)$ plane, corresponding to ``weak'' and ``strong'' violations of linear response under a change in magnetic field, are shown to have the same functional form as the de Almeida-Thouless critical line. Our results demonstrate the existence of a fundamental link between static and dynamic properties of spin glasses, predicted by the mean-field theory of aging phenomena.Comment: 9 pages, 10 figure

Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium 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 new results are obtained. The equilibrium two-point scaling functions are obtained. The nonequilibrium, finite momentum, two-time $t,t'$ response and correlations are computed. They are shown to exhibit scaling forms, characterized by novel exponents $\lambda_R \neq \lambda_C$, as well as universal scaling functions that we compute. The fluctuation dissipation ratio is found to be non trivial and of the form $X(q^z (t-t'), t/t')$. Analogies and differences with pure critical models are discussed.Comment: 33 pages, RevTe

There are no magnetically charged particle-like solutions of the Einstein Yang-Mills equations for Abelian models

We prove that there are no magnetically charged particle-like solutions for Abelian models in Einstein Yang-Mills, but for non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.Comment: 48 pages, 1 figur