Marginal States in Mean Field Glasses

We study mean field systems whose free energy landscape is dominated by marginally stable states. We review and develop various techniques to describe such states, elucidating their physical meaning and the interrelation between them. In particular, we give a physical interpretation of the two-group replica symmetry breaking scheme and confirm it by establishing the relation to the cavity method and to the counting of solutions of the Thouless-Anderson-Palmer equations. We show how these methods all incorporate the presence of a soft mode in the free energy landscape and interpret the occurring order parameter functions in terms of correlations between the soft mode and the local magnetizations. The general formalism is applied to the prototypical case of the Sherrington-Kirkpatrick-model where we re-examine the physical properties of marginal states under a new perspective.Comment: 27 pages, 8 figure

Designing a commutative replicated data type

Commuting operations greatly simplify consistency in distributed systems. This paper focuses on designing for commutativity, a topic neglected previously. We show that the replicas of \emph{any} data type for which concurrent operations commute converges to a correct value, under some simple and standard assumptions. We also show that such a data type supports transactions with very low cost. We identify a number of approaches and techniques to ensure commutativity. We re-use some existing ideas (non-destructive updates coupled with invariant identification), but propose a much more efficient implementation. Furthermore, we propose a new technique, background consensus. We illustrate these ideas with a shared edit buffer data type

Exploiting replication in distributed systems

Techniques are examined for replicating data and execution in directly distributed systems: systems in which multiple processes interact directly with one another while continuously respecting constraints on their joint behavior. Directly distributed systems are often required to solve difficult problems, ranging from management of replicated data to dynamic reconfiguration in response to failures. It is shown that these problems reduce to more primitive, order-based consistency problems, which can be solved using primitives such as the reliable broadcast protocols. Moreover, given a system that implements reliable broadcast primitives, a flexible set of high-level tools can be provided for building a wide variety of directly distributed application programs

Low temperature spin glass fluctuations: expanding around a spherical approximation

The spin glass behavior near zero temperature is a complicated matter. To get an easier access to the spin glass order parameter $Q(x)$ and, at the same time, keep track of $Q_{ab}$, its matrix aspect, and hence of the Hessian controlling stability, we investigate an expansion of the replicated free energy functional around its ``spherical'' approximation. This expansion is obtained by introducing a constraint-field and a (double) Legendre Transform expressed in terms of spin correlators and constraint-field correlators. The spherical approximation has the spin fluctuations treated with a global constraint and the expansion of the Legendre Transformed functional brings them closer and closer to the Ising local constraint. In this paper we examine the first contribution of the systematic corrections to the spherical starting point.Comment: 16 pages, 2 figure

Optimisation problems and replica symmetry breaking in finite connectivity spin-glasses

A formalism capable of handling the first step of hierarchical replica symmetry breaking in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field distributions (or, equivalently magnetisation distributions) inside the cluster of states. The approach is shown to coincide with the previous works in the replica symmetric case and in the two limit cases m=0,1 where m is Parisi's break-point. As an application to the study of optimization problems, the ground-state properties of the random 3-Satisfiability problem are investigated and we present a first RSB solution improving replica symmetric results.Comment: 16 pages Revtex file, 1 figure; amended version with two new appendices; to be published in J.Phys.

On Equilibrium Dynamics of Spin-Glass Systems

We present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ 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 $p$-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 $R$. In the limit $R\to\infty$ 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 $\Delta$ of the Sompolinsky theory.Comment: 24 pages, 6 figure