相关论文: Phase transitions in random Potts systems and the …

We examine phase transitions between the easy, hard, and the unsolvable phases when attempting to identify structure in large complex networks (community detection) in the presence of disorder induced by network noise (spurious links that…

We examine a global disorder transition when identifying community structure in an arbitrary complex network. Earlier, we illustrated [Phil. Mag. 92, 406 (2012)] that "community detection" (CD) generally exhibits disordered (or unsolvable)…

Existing theories explain spin glass transition in terms of a phase transition and order parameters, and assume the existence of a distinct spin glass phase. In addition to problems related to clarifying the nature of this phase, the common…

Recently, it was shown that there is a phase transition in the community detection problem. This transition was first computed using the cavity method, and has been proved rigorously in the case of $q=2$ groups. However, analytic…

Similarities between fragile glasses and spin glasses (SG) suggest the study of frustrated spin model to understand the complex dynamics of glasses above the glass transition. We consider a frustrated spin model with Ising spins and s-state…

Consider a network consisting of two subnetworks (communities) connected by some external edges. Given the network topology, the community detection problem can be cast as a graph partitioning problem that aims to identify the external…

We have studied the Potts spin glass with 2-state Ising spins and s-state Potts variables using a cluster Monte Carlo dynamics. The model recovers the +- J Ising spin glass (SG) for s=1 and exhibits for all s a SG transition at T_{SG}(s)…

We report on an exceptionally accurate spin-glass-type Potts model for community detection. With a simple algorithm, we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of…

Potts glasses are prototype models that have been used to understand the structural glass transition. However, in finite space dimensions a glass transition remains to be detected in the 10-state Potts glass. Using a one-dimensional model…

Pinning a fraction of particles from an equilibrium configuration in supercooled liquids has been recently proposed as a way to induce a new kind of glass transition, the Random Pinning Glass Transition (RPGT). The RPGT has been predicted…

Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low…

We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks. Our results are also applicable to detection of functional modules, partitions, and colorings in noisy planted models. Using a…

Recently, a phase transition has been discovered in the network community detection problem below which no algorithm can tell which nodes belong to which communities with success any better than a random guess. This result has, however, so…

The description of thermodynamic phase transitions in terms of percolation transitions of suitably defined clusters has a long tradition and boasts a number of important successes, the most prominent ones being in ferromagnetic lattice…

The glass transition is considered within two toys models, a mean field spin glass and a directed polymer in a correlated random potential. In the spin glass model there occurs a dynamical transition, where the system condenses in a state…

Community detection in graphs is the problem of finding groups of vertices which are more densely connected than they are to the rest of the graph. This problem has a long history, but it is undergoing a resurgence of interest due to the…

Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a new framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of…

We demonstrate the real-time detection of dynamical phase transitions (DPTs) in lattice-confined spinor gases subject to a priori unknown time-variant interactions, via the temporal behaviors of both the system energy and spinor phases…

Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…

A fast community detection algorithm based on a q-state Potts model is presented. Communities in networks (groups of densely interconnected nodes that are only loosely connected to the rest of the network) are found to coincide with the…