556 research outputs found
Finite dimensional corrections to mean field in a short-range p-spin glassy model
In this work we discuss a short range version of the -spin model. The
model is provided with a parameter that allows to control the crossover with
the mean field behaviour. We detect a discrepancy between the perturbative
approach and numerical simulation. We attribute it to non-perturbative effects
due to the finite probability that each particular realization of the disorder
allows for the formation of regions where the system is less frustrated and
locally freezes at a higher temperature.Comment: 18 pages, 5 figures, submitted to Phys Rev
On Equilibrium Dynamics of Spin-Glass Systems
We present a critical analysis of the Sompolinsky theory of equilibrium
dynamics. By using the spherical spin glass model we test the asymptotic
static limit of the Sompolinsky solution showing that it fails to yield a
thermodynamically stable solution. We then present an alternative formulation,
based on the Crisanti, H\"orner and Sommers [Z. f\"ur Physik {\bf 92}, 257
(1993)] dynamical solution of the spherical -spin spin glass model,
reproducing a stable static limit that coincides, in the case of a one step
Replica Symmetry Breaking Ansatz, with the solution at the dynamic free energy
threshold at which the relaxing system gets stuck off-equilibrium. We formally
extend our analysis to any number of Replica Symmetry Breakings . In the
limit both formulations lead to the Parisi anti-parabolic
differential equation. This is the special case, though, where no dynamic
blocking threshold occurs. The new formulation does not contain the additional
order parameter of the Sompolinsky theory.Comment: 24 pages, 6 figure
Growth and Inequality: A Meta-Analysis
In recent years there has been a growing interest in the impact of inequality on economic growth. Both theoretical and empirical approaches have produced ambiguous results on sign and size of this relationship. Although there is a considerable part of the literature that considers inequality detrimental to growth, more recent studies have challenged this result and found a positive effect of inequality on growth. This paper contributes to the debate by using meta-analytical techniques to describe variation in observed outcomes of the empirical studies and to identify sources of variation
Local excitations in mean field spin glasses
We address the question of geometrical as well as energetic properties of
local excitations in mean field Ising spin glasses. We study analytically the
Random Energy Model and numerically a dilute mean field model, first on
tree-like graphs, equivalent to a replica symmetric computation, and then
directly on finite connectivity random lattices. In the first model,
characterized by a discontinuous replica symmetry breaking, we found that the
energy of finite volume excitation is infinite whereas in the dilute mean field
model, described by a continuous replica symmetry breaking, it slowly decreases
with sizes and saturates at a finite value, in contrast with what would be
naively expected. The geometrical properties of these excitations are similar
to those of lattice animals or branched polymers. We discuss the meaning of
these results in terms of replica symmetry breaking and also possible relevance
in finite dimensional systems.Comment: 7 pages, 4 figures, accepted for publicatio
Is the droplet theory for the Ising spin glass inconsistent with replica field theory?
Symmetry arguments are used to derive a set of exact identities between
irreducible vertex functions for the replica symmetric field theory of the
Ising spin glass in zero magnetic field. Their range of applicability spans
from mean field to short ranged systems in physical dimensions. The replica
symmetric theory is unstable for d>8, just like in mean field theory. For 6<d<8
and d<6 the resummation of an infinite number of terms is necessary to settle
the problem. When d<8, these Ward-like identities must be used to distinguish
an Almeida-Thouless line from the replica symmetric droplet phase.Comment: 4 pages. Accepted for publication in J.Phys.A. This is the accepted
version with the following minor changes: one extra sentence in the abstract;
footnote 2 slightly extended; last paragraph somewhat reformulate
Bayesian joint models with INLA exploring marine mobile predator-prey and competitor species habitat overlap
EPSRC grant Ecowatt 2050 EP/K012851/1 ACKNOWLEDGMENTS We would like to thank the associate editor and the anonymous reviewers for their useful and constructive suggestions which led to a considerable improvement of the manuscript. The authors would also like to thank the following people/organizations for making large datasets available for use in this paper: Mark Lewis (Joint Nature Conservation Committee), Philip Hammond (Scottish Oceans Institute, University of St. Andrews), Susan Lusseau (Marine Scotland Science), Darren Stevens (The Sir Alister Hardy Foundation for Ocean Science, PML), and Yuri Artioli (Plymouth Marine Laboratory). This work was supported by the Engineering and Physical Sciences Research Council (EcoWatt250; EPSRC EP/K012851/1).Peer reviewedPublisher PD
Statistical mechanics of the random K-SAT model
The Random K-Satisfiability Problem, consisting in verifying the existence of
an assignment of N Boolean variables that satisfy a set of M=alpha N random
logical clauses containing K variables each, is studied using the replica
symmetric framework of diluted disordered systems. We present an exact
iterative scheme for the replica symmetric functional order parameter together
for the different cases of interest K=2, K>= 3 and K>>1. The calculation of the
number of solutions, which allowed us [Phys. Rev. Lett. 76, 3881 (1996)] to
predict a first order jump at the threshold where the Boolean expressions
become unsatisfiable with probability one, is thoroughly displayed. In the case
K=2, the (rigorously known) critical value (alpha=1) of the number of clauses
per Boolean variable is recovered while for K>=3 we show that the system
exhibits a replica symmetry breaking transition. The annealed approximation is
proven to be exact for large K.Comment: 34 pages + 1 table + 8 fig., submitted to Phys. Rev. E, new section
added and references update
Computing minimal finite free resolutions
AbstractIn this paper we address the basic problem of computing minimal finite free resolutions of homogeneous submodules of graded free modules over polynomial rings. We develop a strategy, which keeps the resolution minimal at every step. Among the relevant benefits is a marked saving of time, as the first reported experiments in CoCoA show. The algorithm has been optimized using a variety of techniques, such as minimizing the number of critical pairs and employing an “ad hoc” Hilbert-driven strategy. The algorithm can also take advantage of various a priori pieces of information, such as the knowledge of the Castelnuovo regularity
Quenched Random Graphs
Spin models on quenched random graphs are related to many important
optimization problems. We give a new derivation of their mean-field equations
that elucidates the role of the natural order parameter in these models.Comment: 9 pages, report CPTH-A264.109
The Complexity of Ising Spin Glasses
We compute the complexity (logarithm of the number of TAP states) associated
with minima and index-one saddle points of the TAP free energy. Higher-index
saddles have smaller complexities. The two leading complexities are equal,
consistent with the Morse theorem on the total number of turning points, and
have the value given in [A. J. Bray and M. A. Moore, J. Phys. C 13, L469
(1980)]. In the thermodynamic limit, TAP states of all free energies become
marginally stable.Comment: Typos correcte
- …