اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGrowing dynamical length, scaling and heterogeneities in the 3d Edwards-Anderson model
140
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study numerically spatio-temporal fluctuations during the out-of-equilibrium relaxation of the three-dimensional Edwards-Anderson model. We focus on two issues. (1) The evolution of a growing dynamical length scale in the glassy phase of the model, and the consequent collapse of the distribution of local coarse-grained correlations measured at different pairs of times on a single function using {it two} scaling parameters, the value of the global correlation at the measuring times and the ratio of the coarse graining length to the dynamical length scale (in the thermodynamic limit). (2) The `triangular relation between coarse-grained local correlations at three pairs of times taken from the ordered instants $t_3 leq t_2 leq t_1$. Property (1) is consistent with the conjecture that the development of time-reparametrization invariance asymptotically is responsible for the main dynamic fluctuations in aging glassy systems as well as with other mechanisms proposed in the literature. Property (2), we stress, is a much stronger test of the relevance of the time-reparametrization invariance scenario.
قيم البحث
اقرأ أيضاً
We study the off-equilibrium dynamics of the three-dimensional Ising spin glass in the presence of an external magnetic field. We have performed simulations both at fixed temperature and with an annealing protocol. Thanks to the Janus special-purpose
computer, based on FPGAs, we have been able to reach times equivalent to 0.01 seconds in experiments. We have studied the system relaxation both for high and for low temperatures, clearly identifying a dynamical transition point. This dynamical temperature is strictly positive and depends on the external applied magnetic field. We discuss different possibilities for the underlying physics, which include a thermodynamical spin-glass transition, a mode-coupling crossover or an interpretation reminiscent of the random first-order picture of structural glasses.
In the Edwards-Anderson model of spin glasses with a bimodal distribution of bonds, the degeneracy of the ground state allows one to define a structure called backbone, which can be characterized by the rigid lattice (RL), consisting of the bonds tha
t retain their frustration (or lack of it) in all ground states. In this work we have performed a detailed numerical study of the properties of the RL, both in two-dimensional (2D) and three-dimensional (3D) lattices. Whereas in 3D we find strong evidence for percolation in the thermodynamic limit, in 2D our results indicate that the most probable scenario is that the RL does not percolate. On the other hand, both in 2D and 3D we find that frustration is very unevenly distributed. Frustration is much lower in the RL than in its complement. Using equilibrium simulations we observe that this property can be found even above the critical temperature. This leads us to propose that the RL should share many properties of ferromagnetic models, an idea that recently has also been proposed in other contexts. We also suggest a preliminary generalization of the definition of backbone for systems with continuous distributions of bonds, and we argue that the study of this structure could be useful for a better understanding of the low temperature phase of those frustrated models.
We study the performance of different message passing algorithms in the two dimensional Edwards Anderson model. We show that the standard Belief Propagation (BP) algorithm converges only at high temperature to a paramagnetic solution. Then, we test a
Generalized Belief Propagation (GBP) algorithm, derived from a Cluster Variational Method (CVM) at the plaquette level. We compare its performance with BP and with other algorithms derived under the same approximation: Double Loop (DL) and a two-ways message passing algorithm (HAK). The plaquette-CVM approximation improves BP in at least three ways: the quality of the paramagnetic solution at high temperatures, a better estimate (lower) for the critical temperature, and the fact that the GBP message passing algorithm converges also to non paramagnetic solutions. The lack of convergence of the standard GBP message passing algorithm at low temperatures seems to be related to the implementation details and not to the appearance of long range order. In fact, we prove that a gauge invariance of the constrained CVM free energy can be exploited to derive a new message passing algorithm which converges at even lower temperatures. In all its region of convergence this new algorithm is faster than HAK and DL by some orders of magnitude.
The stability of the spin-glass phase against a magnetic field is studied in the three and four dimensional Edwards-Anderson Ising spin glasses. Effective couplings and effective fields associated with length scale L are measured by a numerical domai
n-wall renormalization group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H goes to zero but remains finite for any non-zero H, implying that the spin-glass phase is absent even in an infinitesimal field. These results are well consistent with the droplet theory for short-range spin glasses.
A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow
particles and determine their size, $N_c$, and their radius of gyration, $R_G$. We show that $N_cpropto R_G^{d_f}$, providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, $d_f$, that is observed to increase with packing fraction $phi$. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., $phitophi_c$. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor $S_4(q,t)$ and the dynamical susceptibility $chi_4(t)$. $S_4(q,t)$ is shown to obey scaling in the full range of packing fractions, $0.6leqphileq 0.805$, and to become increasingly long-ranged as $phitophi_c$. Finite size scaling of $chi_4(t)$ provides a consistency check for the previously analyzed divergences of $chi_4(t)propto (phi-phi_c)^{-gamma_{chi}}$ and the correlation length $xipropto (phi-phi_c)^{-gamma_{xi}}$. We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for $phitophi_c$ suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
