Related papers: Phase Transitions on Random Lattices: How Random i…
Discontinuous transitions have received considerable interest due to the uncovering that many phenomena such as catastrophic changes, epidemic outbreaks and synchronization present a behavior signed by abrupt (macroscopic) changes (instead…
The quantum phase transition between two clean, non interacting topologically distinct gapped states in three dimensions is governed by a massless Dirac fermion fixed point, irrespective of the underlying symmetry class, and this…
We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and…
Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by…
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…
The Voronoi construction is ubiquitous across the natural sciences and engineering. In statistical mechanics, though, critical phenomena have so far been only investigated on the Delaunay triangulation, the dual of a Voronoi graph. In this…
We address issues related to the presence of defects at finite-temperature topological transitions, in particular when defects are modeled in terms of further variables associated with a quenched disorder, corresponding to the limit in…
We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale…
The vortex lattice is an ideal system to study the competition and interplay between interaction and disorder. New results on 2H-NbSe_2 (in samples of progressively increasing pinning) elucidate how pinning alters the phase boundary…
To better understand the temporal characteristics and the lifetime of fluctuations in stochastic processes in networks, we investigated diffusive persistence in various graphs. Global diffusive persistence is defined as the fraction of…
Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped 2-d system of particles interacting by repulsive forces. As a…
We explore the impact of social noise, characterized by nonconformist behavior, on the phase transition within the framework of the majority rule model. The order-disorder transition can reflect the consensus-polarization state in a social…
We present a stochastic algorithm for constructing a topologically disordered (i.e., non-regular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier…
The density and correlations of topological defects are investigated numerically in a model of a d=2 elastic medium subject to a periodic quenched random potential. The computed density of defects decreases approximately exponentially with…
We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in (2+1)d. TDP is defined as the constant correction that appears in the…
Two-dimensional topological insulators are characterized by an insulating bulk and conductive edge states protected by the nontrivial topology of the bulk electronic structure. They remain robust against moderate disorder until Anderson…
We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such "random-field" disorder…
We study a periodically driven one dimensional Kitaev model in the presence of disorder. In the clean limit our model exhibits four topological phases corresponding to the existence or non-existence of edge modes at zero and pi quasienergy.…
We have studied a two dimensional lattice model of Coulomb glass for a wide range of disorders at $T\sim 0$. The system was first annealed using Monte Carlo simulation. Further minimization of the total energy of the system was done using…
The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…