Related papers: On the freezing of variables in random constraint …
We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a…
Models of confluent tissues are built out of tessellations of the space (both in two and three dimensions) in which the cost function is constructed in such a way that individual cells try to optimize their volume and surface in order to…
Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical…
A disordered spin model suitable for studying inverse freezing in fragile glass-forming systems is introduced. The model is a microscopic realization of the ``random-first order'' scenario in which the glass transition can be either…
The correlations of the free-energy landscape of mean-field spin glasses at different temperatures are investigated, concentrating on models with a first order freezing transition. Using a ``potential function'' we follow the metastable…
We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations.…
We use computer simulations to investigate the static properties of a simple glass-forming fluid in which the positions of a finite fraction of the particles has been frozen in. By probing the equilibrium distribution of the overlap between…
The properties of a macroscopic assembly of weakly-repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits a quantum transition from superfluid to…
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
Despite the extreme simplicity in their definition, spin glasses disclose a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis we try to shed light on some of them, focusing on one hand on the search of…
A solution to a 3-satisfiability (3-SAT) formula can be expanded into a cluster, all other solutions of which are reachable from this one through a sequence of single-spin flips. Some variables in the solution cluster are frozen to the same…
Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to…
Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…
The dynamical transition occurring in spin-glass models with one step of Replica-Symmetry-Breaking is a mean-field artifact that disappears in finite systems and/or in finite dimensions. The critical fluctuations that smooth the transition…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
We develop a real space renormalisation group analysis of disordered models of glasses, in particular of the spin models at the origin of the Random First Order Transition theory. We find three fixed points respectively associated to the…
A recently introduced Renormalization Group approach to frustrated spin models is applied in three dimensions through Monte Carlo computations. A class of spin glass models is analysed, with correlated disorder variables given by a Z_2…
Planting a solution into the random RB model, which is a prototype of random constraint satisfaction problem (CSP) with growing domains, can generate very hard satisfiable CSP benchmarks. We study the solution space structure of the planted…