14 research outputs found
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 non trivial 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.Comment: 13 pages, 1 figur
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 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 are recovered and
several new results are obtained. The equilibrium two-point scaling functions
are obtained. The nonequilibrium, finite momentum, two-time response and
correlations are computed. They are shown to exhibit scaling forms,
characterized by novel exponents , as well as
universal scaling functions that we compute. The fluctuation dissipation ratio
is found to be non trivial and of the form . Analogies and
differences with pure critical models are discussed.Comment: 33 pages, RevTe
Spatially heterogeneous ages in glassy dynamics
We construct a framework for the study of fluctuations in the nonequilibrium
relaxation of glassy systems with and without quenched disorder. We study two
types of two-time local correlators with the aim of characterizing the
heterogeneous evolution: in one case we average the local correlators over
histories of the thermal noise, in the other case we simply coarse-grain the
local correlators. We explain why the former describe the fingerprint of
quenched disorder when it exists, while the latter are linked to noise-induced
mesoscopic fluctuations. We predict constraints on the pdfs of the fluctuations
of the coarse-grained quantities. We show that locally defined correlations and
responses are connected by a generalized local out-of-equilibrium
fluctuation-dissipation relation. We argue that large-size heterogeneities in
the age of the system survive in the long-time limit. The invariance of the
theory under reparametrizations of time underlies these results. We relate the
pdfs of local coarse-grained quantities and the theory of dynamic random
manifolds. We define a two-time dependent correlation length from the spatial
decay of the fluctuations in the two-time local functions. We present numerical
tests performed on disordered spin models in finite and infinite dimensions.
Finally, we explain how these ideas can be applied to the analysis of the
dynamics of other glassy systems that can be either spin models without
disorder or atomic and molecular glassy systems.Comment: 47 pages, 60 Fig