1,124 research outputs found
How a spin-glass remembers. Memory and rejuvenation from intermittency data: an analysis of temperature shifts
The memory and rejuvenation aspects of intermittent heat transport are
explored theoretically and by numerical simulation for Ising spin glasses with
short-ranged interactions. The theoretical part develops a picture of
non-equilibrium glassy dynamics recently introduced by the authors. Invoking
the concept of marginal stability, this theory links irreversible
`intermittent' events, or `quakes' to thermal fluctuations of record magnitude.
The pivotal idea is that the largest energy barrier surmounted prior
to by thermal fluctuations at temperature determines the rate of the intermittent events occurring near . The idea leads
to a rate of intermittent events after a negative temperature shift given by
, where the `effective age' has
an algebraic dependence on , whose exponent contains the temperatures
before and after the shift. The analytical expression is verified by numerical
simulations. Marginal stability suggests that a positive temperature shift could erase the memory of the barrier . The simulations show
that the barrier controls the intermittent dynamics,
whose rate is hence .
Additional `rejuvenation' effects are also identified in the intermittency
data for shifts of both signs.Comment: Revised introduction and discussion. Final version to appear in
Journal of Statistical Mechanics: Theory and Experimen
Extremal statistics of curved growing interfaces in 1+1 dimensions
We study the joint probability distribution function (pdf) of the maximum M
of the height and its position X_M of a curved growing interface belonging to
the universality class described by the Kardar-Parisi-Zhang equation in 1+1
dimensions. We obtain exact results for the closely related problem of p
non-intersecting Brownian bridges where we compute the joint pdf P_p(M,\tau_M)
where \tau_M is there the time at which the maximal height M is reached. Our
analytical results, in the limit p \to \infty, become exact for the interface
problem in the growth regime. We show that our results, for moderate values of
p \sim 10 describe accurately our numerical data of a prototype of these
systems, the polynuclear growth model in droplet geometry. We also discuss
applications of our results to the ground state configuration of the directed
polymer in a random potential with one fixed endpoint.Comment: 6 pages, 4 figures. Published version, to appear in Europhysics
Letters. New results added for non-intersecting excursion
The critical Z-invariant Ising model via dimers: the periodic case
We study a large class of critical two-dimensional Ising models namely
critical Z-invariant Ising models on periodic graphs, example of which are the
classical square, triangular and honeycomb lattice at the critical temperature.
Fisher introduced a correspondence between the Ising model and the dimer model
on a decorated graph, thus setting dimer techniques as a powerful tool for
understanding the Ising model. In this paper, we give a full description of the
dimer model corresponding to the critical Z-invariant Ising model. We prove
that the dimer characteristic polynomial is equal (up to a constant) to the
critical Laplacian characteristic polynomial, and defines a Harnack curve of
genus 0. We prove an explicit expression for the free energy, and for the Gibbs
measure obtained as weak limit of Boltzmann measures.Comment: 35 pages, 8 figure
Cluster size distributions in particle systems with asymmetric dynamics
We present exact and asymptotic results for clusters in the one-dimensional
totally asymmetric exclusion process (TASEP) with two different dynamics. The
expected length of the largest cluster is shown to diverge logarithmically with
increasing system size for ordinary TASEP dynamics and as a logarithm divided
by a double logarithm for generalized dynamics, where the hopping probability
of a particle depends on the size of the cluster it belongs to. The connection
with the asymptotic theory of extreme order statistics is discussed in detail.
We also consider a related model of interface growth, where the deposited
particles are allowed to relax to the local gravitational minimum.Comment: 12 pages, 3 figures, RevTe
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