Related papers: Phase Transitions and Computational Difficulty in …
Phase transitions in spin glass type systems and, more recently, in related computational problems have gained broad interest in disparate arenas. In the current work, we focus on the "community detection" problem when cast in terms of a…
I review recent developments in determining the QCD phase diagram by means of lattice simulations. Since the invention of methods to side-step the sign problem a few years ago, a number of additional variants have been proposed, and…
Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed,…
For many random Constraint Satisfaction Problems, by now, we have asymptotically tight estimates of the largest constraint density for which they have solutions. At the same time, all known polynomial-time algorithms for many of these…
Quantum systems with geometrical frustration remain an outstanding challenge for numerical simulations due to the infamous numerical sign problem. Here, we overcome this obstruction via complex path integration in a geometrically frustrated…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behavior of particles in neutron…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
After reviewing the basics of the cavity method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of spins with random ferromagnetic interactions and a random…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
We study the problem of bicoloring random hypergraphs, both numerically and analytically. We apply the zero-temperature cavity method to find analytical results for the phase transitions (dynamic and static) in the 1RSB approximation. These…
The multi-index matching is an NP-hard combinatorial optimization problem; for two indices it reduces to the well understood bipartite matching problem that belongs to the polynomial complexity class. We use the cavity method to solve the…
Using T=0 Monte Carlo simulation, we study the relaxation of graph coloring (K-COL) and satisfiability (K-SAT), two hard problems that have recently been shown to possess a phase transition in solvability as a parameter is varied. A change…
Phase diagrams chart material properties with respect to one or more external or internal parameters such as pressure or magnetisation; as such, they play a fundamental role in many theoretical and applied fields of science. In this work,…
We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem…
A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite…
The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a…
We analyse the motion of a system of particles subjected a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition: the…