Related papers: Reply to the comment by Jacobs and Thorpe

We study the phase transition of the three-dimensional complex |psi|^4 theory by considering the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using…

The q-state Potts model can be formulated in geometric terms, with Fortuin-Kasteleyn (FK) clusters as fundamental objects. If the phase transition of the model is second order, it can be equivalently described as a percolation transition of…

Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…

Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…

Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…

The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…

This paper explores the link between the ergodicity of the clus-ter equivalence relation restricted to its infinite locus and the indis-tinguishability of infinite clusters. It is an important element of the dictionary connecting orbit…

Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…

We consider geometrical characteristics of monopole clusters of the lattice SU(2) gluodynamics. We argue that the polymer approach to the field theory is an adequate means to describe the monopole clusters. Both finite-size and the…

Tunable mechanics and fracture resistance are hallmarks of biological tissues and highly desired in engineered materials. To elucidate the underlying mechanisms, we study a rigidly percolating double network (DN) made of a stiff and a…

We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an…

Many systems such as critical infrastructure exhibit a modular structure with many links within the modules and few links between them. One approach to increase the robustness of these systems is to reinforce a fraction of the nodes in each…

These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…

Recently much attention has been paid to the study of the robustness of interdependent and multiplex networks and, in particular, networks of networks. The robustness of interdependent networks can be evaluated by the size of a mutually…

We review the analysis of polarized structure function data using perturbative QCD at next-to-leading order. We use the most recent experimental data to obtain updated results for polarized parton distributions, first moments and the strong…

Comment on O. Gendelman, Y. G. Pollack, I. Procaccia, S. Sengupta, and J. Zylberg, Physical Review Letters 116, 078001 (2016).

We study the nature of the frictional jamming transition within the framework of rigidity percolation theory. Slowly sheared frictional packings are decomposed into rigid clusters and floppy regions with a generalization of the pebble game…

The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…

The ``crumpling" transition, between rigid and crumpled surfaces, has been object of much discussion over the past years. The common lore is that such transition should be of second order. However, some lattice versions of the rigidity term…

Reply to the comment, cond-mat/0209398 by by N.W. Watkins, S.C. Chapman, and G. Rowlands