1,721,022 research outputs found
Enhancement of structural rearrangement in glassy systems under shear flow
No full textWe extend the analysis of the mean field schematic model
recently introduced (see Corberi F., Nicodemi M., Piccioni M. and Coniglio A.
Phys. Rev. Lett., 83 (1999) 5054)
for the description of
glass forming liquids to the case of a supercooled fluid
subjected to a shear flow
of rate γ.
After quenching the system to a low temperature T,
a slow glassy regime is observed before
stationarity is achieved at the characteristic
time \tau _\ab{g}.
\tau _\ab{g} is of the order of the
usual equilibration time without shear \tau _\ab{g}^0
for weak shear,
\gamma \tau _\ab{g} ^0<1. For larger
shear, \gamma \tau _\ab{g} ^0>1,
local rearrangement of dense regions is instead enhanced
by the flow, and \tau_\ab{g} \simeq 1/(T\gamma)
General properties of the response function in a class of solvable non-equilibrium models
No full textWe study the non-equilibrium response function R i j ( t , t ′ ) , namely the variation of the local magnetization ⟨ S i ( t ) ⟩ on site i at time t as an effect of a perturbation applied at the earlier time t′ on site j, in a class of solvable spin models characterized by the vanishing of the so-called asymmetry. This class encompasses both systems brought out of equilibrium by the variation of a thermodynamic control parameter, as after a temperature quench, or intrinsically out of equilibrium models with violation of detailed balance. The one-dimensional Ising model and the voter model (on an arbitrary graph) are prototypical examples of these two situations which are used here as guiding examples. Defining the fluctuation-dissipation ratio X i j ( t , t ′ ) = β R i j / ( ∂ G i j / ∂ t ′ ) , where G i j ( t , t ′ ) = ⟨ S i ( t ) S j ( t ′ ) ⟩ is the spin-spin correlation function and β is a parameter regulating the strength of the perturbation (corresponding to the inverse temperature when detailed balance holds), we show that, in the quite general case of a kinetics obeying dynamical scaling, on equal sites this quantity has a universal form X i i ( t , t ′ ) = ( t + t ′ ) / ( 2 t ) , whereas lim t → ∞ X i j ( t , t ′ ) = 1 / 2 for any ij couple. The specific case of voter models with long-range interactions is thoroughly discussed
Emergence of correlations in highly biased Consensus Models in seed initial configuration
No full textWe study the consensus probability in Voter Model and Invasion Process starting from a seed initial configuration. In the case where the opinions have the same strength or slightly different (weak bias) this function was computed analytically by Sood, Antal and Redner and depends only on the degree of the promoter individual. We check numerically through large scale simulations the above mentioned theory and we find that in the case of strong bias a correlation between the consensus probability and other centrality measures emerge and Sood et al's theory is broken
Quasideterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets
No full textWe discuss the interplay between the degree of dynamical stochasticity, memory persistence, and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory effects, which correspond to the slowest possible temporal decay of the correlation function, are accompanied by the largest possible violation of self-averaging and a quasideterministic descent into the ergodic components. This phenomenon is observed in different systems, such as the Ising model with long-range interactions, including the mean-field, and the short-range random-field Ising model
Universality in the time correlations of the long-range 1d Ising model
No full textThe equilibrium and nonequilibrium properties of ferromagnetic systems may be affected by the long-range nature of the coupling interaction. Here we study the phase separation process of a one-dimensional Ising model in the presence of a power-law decaying coupling, J(r)=1/r1+σ with σ>0, and we focus on the two-time autocorrelation function C(t,tw)=⟨si(t)si(tw)⟩. We find that it obeys the scaling form C(t,tw)=f(L(tw)/L(t)), where L(t) is the typical domain size at time t, and where f(x) can only be of two types. For σ>1, when domain walls diffuse freely, f(x) falls in the nearest-neighbour (nn) universality class. Conversely, for σ≤1, when domain walls dynamics is driven, f(x) displays a new universal behavior. In particular, the so-called Fisher-Huse exponent, which characterizes the asymptotic behavior of f(x)≃x−λ for x≫1, is λ=1 in the nn universality class (σ>1) and λ=1/2 for σ≤1
Coarsening and metastability of the long-range voter model in three dimensions
No full textWe study analytically the ordering kinetics and the final metastable states in the three-dimensional long-range voter model where N agents described by a boolean spin variable S-i can be found in two states (or opinion) +/- 1. The kinetics is such that each agent copies the opinion of another at distance r chosen with probability P(r) proportional to r(-alpha) (a > 0). In the thermodynamic limit N ->infinity the system approaches a correlated metastable state without consensus, namely without full spin alignment. In such states the equal-time correlation function C(r) = < SiSj > (where r is the i-j distance) decrease algebraically in a slow, non-integrable way. Specifically, we find C(r) similar to r(-1), or C(r)similar to r(6-a), or C(r)similar to r(-a) for a >5, 3< a <= 5 and 0 <= <= a <= 3, respectively. In a finite system metastability is escaped after a time of order N and full ordering is eventually achieved. The dynamics leading to metastability is of the coarsening type, with an ever increasing correlation length L(t) (for N ->infinity). We find L(t)similar to t1/2 for a <= 5 L(t)similar to t5{2\al}}4<\al \le 53\le \al \le 40\le \al < 3$ there is not macroscopic coarsening because stationarity is reached in a microscopic time. Such results allow us to conjecture the behavior of the model for generic space dimension
Ordering kinetics with long-range interactions: interpolating between voter and Ising models
No full textWe study the ordering kinetics of a generalization of the voter model with long-range interactions, the p-voter model, in one dimension. It is defined in terms of Boolean variables S-i, agents or spins, located on sites i of a lattice, each of which takes in an elementary move the state of the majority of p other agents at distances r chosen with probability P(r)proportional to r(-alpha). For p = 2 the model can be exactly mapped onto the case with p = 1, which amounts to the voter model with long-range interactions decaying algebraically. For 3 <= p < infinity, instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant J(r) = P(r) quenched to small finite temperatures. In the limit p -> infinity, a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for p > 3 a closed set of differential equations cannot be found, we employed numerical simulations to address this case
Quasideterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets
No full textWe discuss the interplay between the degree of dynamical stochasticity, memory persistence, and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory effects, which correspond to the slowest possible temporal decay of the correlation function, are accompanied by the largest possible violation of self-averaging and a quasideterministic descent into the ergodic components. This phenomenon is observed in different systems, such as the Ising model with long-range interactions, including the mean-field, and the short-range random-field Ising model
Thermalization with a multibath: an investigation in simple models
No full textWe study analytically and numerically a couple of paradigmatic spin models, each described in terms of two sets of variables attached to two different thermal baths with characteristic timescales T and τ and inverse temperatures B and β. In the limit in which one bath becomes extremely slow ( τ → ∞ ), such models amount to a paramagnet and to a one-dimensional ferromagnet in contact with a single bath. Our study is also motivated by analogies with disordered systems where widely separated timescales associated with different effective temperatures emerge. We show that these systems reach a stationary state in a finite time for any choice of B and β. We determine the non-equilibrium fluctuation-dissipation relation between the autocorrelation and the response function in such a state and, from that, we discuss if and how thermalization with the two baths occurs and the emergence of a non-trivial fluctuation-dissipation ratio
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