Related papers: On the freezing of variables in random constraint …
We investigate scaling limits of trees built by uniform attachment with freezing, which is a variant of the classical model of random recursive trees introduced in a companion paper. Here vertices are allowed to freeze, and arriving…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
A class of models with self-generated disorder and controlled frustration is studied. Between the trivial case, where frustration is not present at all, and the limit case, where frustration is present over every length scale, a region with…
In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether…
We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external,…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…
We consider a system of spherical particles interacting by means of a pair potential equal to a finite constant for interparticle distances smaller than the sphere diameter and zero outside. The model may be a prototype for the interaction…
We study a system of penetrable bosons on a line, focusing on the high-density/weak-interaction regime, where the ground state is, to a good approximation, a condensate. Under compression, the system clusterizes at zero temperature, i.e.,…
We calculate moments of free energy's finite size correction for the transition point between ferromagnetic and spin glass phases. We find, that those moments scale with the number of spins with different critical indices, characteristic…
In a spin glass system on a random graph, some vertices have their spins changing among different configurations of a ground--state domain. Long range frustrations may exist among these unfrozen vertices in the sense that certain…
We study the effect of freezing the positions of a fraction $c$ of particles from an equilibrium configuration of a supercooled liquid at a temperature $T$. We show that within the Random First-Order Transition theory pinning particles…
Monte Carlo sampling of any system may be analyzed in terms of an associated glass model -- a variant of the Random Energy Model -- with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen…
We study the set of solutions of random k-satisfiability formulae through the cavity method. It is known that, for an interval of the clause-to-variables ratio, this decomposes into an exponential number of pure states (clusters). We refine…
Spin glasses occupy a unique place in condensed matter: they freeze collectively while remaining struc-turally disordered, and they exhibit slow, history-dependent dynamics that reflect an exceptionally rug-ged free-energy landscape. This…
We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited…
Quantum phase transitions occur at zero temperature and involve the appearance of long-range correlations. These correlations are not due to thermal fluctuations but to the intricate structure of a strongly entangled ground state of the…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
We present a detailed analysis of glass transitions induced by pinning particles at random from an equilibrium configuration. We first develop a mean-field analysis based on the study of p-spin spherical disordered models and then obtain…
We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring…