7,249 research outputs found
On the origin of ultrametricity
In this paper we show that in systems where the probability distribution of
the the overlap is non trivial in the infinity volume limit, the property of
ultrametricity can be proved in general starting from two very simple and
natural assumptions: each replica is equivalent to the others (replica
equivalence or stochastic stability) and all the mutual information about a
pair of equilibrium configurations is encoded in their mutual distance or
overlap (separability or overlap equivalence).Comment: 13 pages, 1 figur
Critical interface: twisting spin glasses at
We consider identical copies of spin glasses in finite dimension coupled at
the boundaries. This allows to identify the spin glass analogous of twisted
boundary conditions in ferromagnetic system and leads to the definition of an
interface free-energy that is positively defined and that should scale with a
positive power of the system size in the spin glass phase. In this note we
study the behavior of the interface at the spin glass critical temperature
within mean field theory. We show that the leading scaling of the
interface free-energy does not depend on replica symmetry breaking, and can be
obtained by simple scaling arguments using a cubic theory for critical spin
glasses.Comment: Final version accepted in PRB. Ref. 7 correcte
Comment to "Packing Hyperspheres in High-Dimensional Euclidean Space"
It is shown that the numerical data in cond-mat/0608362 are in very good
agreement with the predictions of cond-mat/0601573.Comment: comment to cond-mat/0608362; 3 pages, 1 figur
A Numerical Study of Ultrametricity in Finite Dimensional Spin Glasses
We use a constrained Monte Carlo technique to analyze ultrametric features of
a 4 dimensional Edwards-Anderson spin glass with quenched couplings J=\pm 1. We
find that in the large volume limit an ultrametric structure emerges quite
clearly in the overlap of typical equilibrium configurations.Comment: 8 one column pages, latex, 4 figures with epsfig.st
Application of p-adic analysis to models of spontaneous breaking of the replica symmetry
Methods of p-adic analysis are applied to the investigation of the
spontaneous symmetry breaking in the models of spin glasses. A p-adic
expression for the replica matrix is given and moreover the replica matrix in
the models of spontaneous breaking of the replica symmetry in the simplest case
is expressed in the form of the Vladimirov operator of p-adic fractional
differentiation. Also the model of hierarchical diffusion (that was proposed to
describe relaxation of spin glasses) investigated using p-adic analysis.Comment: Latex, 8 page
On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses
We compute and analyze couples of ground states of 3D spin glass systems with
the same quenched noise but periodic and anti-periodic boundary conditions for
different lattice sizes. We discuss the possible different behaviors of the
system, we analyze the average link overlap, the probability distribution of
window overlaps (among ground states computed with different boundary
conditions) and the spatial overlap and link overlap correlation functions. We
establish that the picture based on Replica Symmetry Breaking correctly
describes the behavior of 3D Spin Glasses.Comment: 25 pages with 11 ps figures include
First steps of a nucleation theory in disordered systems
We devise a field theoretical formalism for a microscopic theory of
nucleation processes and phase coexistence in finite dimensional glassy
systems. We study disordered -spin models with large but finite range of
interaction. We work in the framework of glassy effective potential theory
which in mean-field is a non-convex, two minima function of the overlap. We
will associate metastability and phase coexistence with the existence of space
inhomogeneous solution of suitable field equations and we will study the
simplest of such solutions.Comment: 31 pages, 4 figures. Content revised, typos correcte
Interfaces and Lower Critical Dimension in a Spin Glass Model
In this paper we try to estimate the lower critical dimension for replica
symmetry breaking in spin glasses through the calculation of the additional
free-energy required to create a domain wall between two different phases. This
mechanism alone would say that replica symmetry would be restored at the lower
critical dimension .Comment: 14 pages, LaTeX, NORDITA preprint 94/2
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