Related papers: Annealed averages in spin and matrix models
In these two lectures I review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
An improved inverse simulated annealing method is presented to determine the structure of complex disordered systems from first principles in agreement with available experimental data or desired predetermined target properties. The…
Active matter, whose motion is driven, and glasses, whose dynamics are arrested, seem to lie at opposite ends of the spectrum in nonequilibrium systems. In spite of this, both classes of systems exhibit a multitude of stable states that are…
Spin glasses have competing interactions that lead to a rough energy landscape which is highly susceptible to small perturbations. These chaotic effects strongly affect numerical simulations and, as such, gaining a deeper understanding of…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
Simulated annealing - moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions - has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers.…
We attempt to give a bird's eye view of the physical mechanisms leading to anomalous relaxation, and the relation of this phenomenon with anomalous diffusion and transport. Whereas in some cases these two notions are indeed deeply related,…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
In this paper we give an elementary approach to several results of Chatterjee in arXiv:0907.3381 and arXiv:1404.7178, as well as some generalizations. First, we prove quenched disorder chaos for the bond overlap in the Edwards-Anderson type…
Understanding how frustration and disorder shape relaxation in complex systems is a central problem in statistical physics and quantum annealing. Spin-glass models provide a natural framework to explore this connection, as their energy…
We revisit the metastability properties of the mixed p-spin spherical disordered models. Firstly, using known methods, we show that there is temperature chaos in a broad range of temperatures. Secondly, we modify the definition of the…
Inspired by striking advances in language modeling, there has recently been much interest in developing autogressive sequence models that are amenable to analytical study. In this short note, we consider extensions of simple disordered…
Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…
A common measure of a function's complexity is the count of its stationary points. For complicated functions, this count grows exponentially with the volume and dimension of their domain. In practice, the count is averaged over a class of…
We present new results reflecting the analogies between the Kob-Andersen model and other glassy systems. Studying the stability of the blocked configurations above and below the transition we also give arguments that supports their…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
Active systems are comprised of constituents with interactions that are generically non-reciprocal in nature. Such non-reciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing…
In this work we study spin-glass (SG) like behavior in the dynamics of multiple agents in a social or economic context using interactions which are similar to the physical case. The different preferences shown by individual agents are…
Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk…
The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement…