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The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method supported by machine learning techniques that is capable of constructing topological models for a generic…
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…
Monte Carlo simulations of the uniformly frustrated 3d XY model are used to model vortex line fluctuations in high temperature superconductors in an applied magnetic field. We find two distinct phase transitions. At a lower T_{c\perp}, the…
The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.
The theory of phase ordering dynamics -- the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase -- is reviewed, with the emphasis on recent developments. Interest will…
As a model to provide a hands-on, elementary understanding of "vortex dynamics", we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex…
We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer…
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…
The pressure-temperature phase diagram of a one-component system, with particles interacting through a spherically symmetric pair potential is studied. It is shown that if the pair potential allows for a discontinuous reduction of the…
We investigate global phase coherence in a system of coupled oscillators on a small-world networks constructed from a ring with nearest-neighbor edges. The effects of both thermal noise and quenched randomness on phase ordering are examined…
We use Monte Carlo simulations of the 3D uniformly frustrated XY model, with uncorrelated quenched randomness in the in-plane couplings, to model the effect of random point pins on the vortex line phases of a type II superconductor. We map…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
Non-linear maps can possess various dynamical behaviors varying from stable steady states and cycles to chaotic oscillations. Most models assume that individuals within a given population are identical ignoring the fundamental role of…
The phase behavior of the lattice restricted primitive model (RPM) for ionic systems with additional short-range nearest neighbor (nn) repulsive interactions has been studied by grand canonical Monte Carlo simulations. We obtain a rich…
Quantum phase transitions between the magnetically ordered and disordered states are studied for the two-dimensional antiferromagnetic quantum spin systems with ladder, plaquette, and mixed-spin structures. Starting with properly chosen…
We analyse features of the patterns formed from a simple model for a martensitic phase transition. This is a fragmentation model that can be encoded by a general branching random walk. An important quantity is the distribution of the…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
The stability of a vortex glass phase with quasi-long-range positional order is examined for a disordered layered superconductor. The role of topological defects is investigated using a detailed scaling argument, supplemented by a…
A coupled map model for the chaotic phase synchronization and its desynchronization phenomenon is proposed. The model is constructed by integrating the coupled kicked oscillator system, kicking strength depending on the complex state…
The emergence of complex modulated structures in the magnetization pattern of thin films is a well-established experimental phenomenology caused by the frustrating effects of competing interactions. Using a coarse-grained version of the…