757 research outputs found
Non trivial overlap distributions at zero temperature
We explore the consequences of Replica Symmetry Breaking at zero temperature.
We introduce a repulsive coupling between a system and its unperturbed ground
state. In the Replica Symmetry Breaking scenario a finite coupling induces a
non trivial overlap probability distribution among the unperturbed ground state
and the one in presence of the coupling. We find a closed formula for this
probability for arbitrary ultrametric trees, in terms of the parameters
defining the tree. The same probability is computed in numerical simulations of
a simple model with many ground states, but no ultrametricity: polymers in
random media in 1+1 dimension. This gives us an idea of what violation of our
formula can be expected in cases when ultrametricity does not hold.Comment: 9 pages, 8 figures; 3 references added, address correcte
Finite-size critical fluctuations in microscopic models of mode-coupling theory
Facilitated spin models on random graphs provide an ideal microscopic
realization of the mode-coupling theory of supercooled liquids: they undergo a
purely dynamic glass transition with no thermodynamic singularity. In this
paper we study the fluctuations of dynamical heterogeneity and their
finite-size scaling properties in the beta relaxation regime of such
microscopic spin models. We compare the critical fluctuations behavior for two
distinct measures of correlations with the results of a recently proposed field
theoretical description based on quasi-equilibrium ideas. We find that the
theoretical predictions perfectly fit the numerical simulation data once the
relevant order parameter is identified with the persistence function of the
spins
Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems
We discuss a resource-competition model, which takes the MacArthur's model as
a platform, to unveil interesting connections with glassy features and jamming
in high dimension. This model presents two qualitatively different phases: a
"shielded" phase, where a collective and self-sustained behavior emerges, and a
"vulnerable" phase, where a small perturbation can destabilize the system and
contribute to population extinction. We first present our perspective based on
a strong similarity with continuous constraint satisfaction problems in their
convex regime. Then, we discuss the stability in terms of the computation of
the leading eigenvalue of the Hessian matrix of the free energy in the replica
space. This computation allows us to efficiently distinguish between the two
aforementioned phases and to relate high-dimensional critical ecosystems to
glassy phenomena in the low-temperature regime.Comment: Updated version with references added. 6 pages, 2 figure
Critical properties of a three dimensional p-spin model
In this paper we study the critical properties of a finite dimensional
generalization of the p-spin model. We find evidence that in dimension three,
contrary to its mean field limit, the glass transition is associated to a
diverging susceptibility (and correlation length).Comment: 6 Pages, 12 Figure
Finite-range spin glasses in the Kac limit: free energy and local observables
We study a finite range spin glass model in arbitrary dimension, where the
intensity of the coupling between spins decays to zero over some distance
. We prove that, under a positivity condition for the interaction
potential, the infinite-volume free energy of the system converges to that of
the Sherrington-Kirkpatrick model, in the Kac limit . We study the
implication of this convergence for the local order parameter, i.e., the local
overlap distribution function and a family of susceptibilities to it
associated, and we show that locally the system behaves like its mean field
analogue. Similar results are obtained for models with -spin interactions.
Finally, we discuss a possible approach to the problem of the existence of long
range order for finite , based on a large deviation functional for
overlap profiles. This will be developed in future work.Comment: 19 pages, revtex
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