相关论文: Phase Transitions and Computational Difficulty in …
We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase…
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…
I review recent progress in numerical simulations of finite temperature quantum chromodynamics and discuss the status of some outstanding problems. Included is (1) a discussion of recent results determining the temperature of the ``phase…
Over the last decade computer simulations have had an increasing role in shedding light on difficult statistical physical phenomena and in particular on the ubiquitous problem of the glass transition. Here in a wide variety of materials the…
The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree \mth{c} is larger than \mth{2.7183}, groups of max-matching patterns which differ greatly from…
The QCD phase diagram in the space of temperature and imaginary baryon chemical potential has been an interesting subject in numerical lattice QCD simulations because of the absence of the sign problem and its deep structure related to…
In this letter, we investigate the ground state properties of an optomechanical system consisting of a coupled cavity and mechanical modes. An exact solution is given when the ratio $\eta$ between the cavity and mechanical frequencies tends…
We discuss an effective theory for QCD at finite chemical potential and non-zero temperature, where QCD is reduced to its center degrees of freedom. The effective action can be mapped to a flux representation, where the complex phase…
We review the recent progress achieved in the theoretical investigation of Quantum Chromodynamics in the high temperature regime, with a focus on results achieved by lattice QCD simulations. The discussion covers the structure of the phase…
In this letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
Phase transition in the two-dimensional $q$-state Potts model with random ferromagnetic couplings in the large-q limit is conjectured to be described by the isotropic version of the infinite randomness fixed point of the random…
In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this…
This theory combines a thermodynamic approach with a dynamic one in order to describe glass transition. Glass transition is regarded as an inaccessible second order phase transition, which is interrupted because of premature critical…
We study the graph alignment problem over two independent Erd\H{o}s-R\'enyi graphs on $n$ vertices, with edge density $p$ falling into two regimes separated by the critical window around $p_c=\sqrt{\log n/n}$. Our result reveals an…
Spin-boson models are essentially useful in the understanding of quantum optics, nuclear physics, quantum dissipation, and quantum computation. We discuss quantum phase transitions in various spin-boson Hamiltonians, compare, and contrast…
Current status of theoretical researches on the QCD phase diagram at finite temperature and baryon chemical potential is reviewed with special emphasis on the origin of various phases and their symmetry breaking patterns. Topics include;…
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…