Related papers: Phase Transitions on Fractals and Networks
For Encyclopedia of Complexity and Systems Science (Springer Verlag). No abstract. I. Definition and Introduction II. Methods III. Quantities and Exponents IV. Fractal Dimension; Incipient Infinite Cluster V. Simple Renormalisation Group…
Fractals are ubiquitous in the natural world, and their connection with phase transitions has been widely observed. This study investigates mechanisms of fractal formation from the perspective of phase transitions. A novel set of…
An outline of recent work on complex networks is given from the point of view of a physicist. Motivation, achievements and goals are discussed with some of the typical applications from a wide range of academic fields. An introduction to…
To understand large, connected systems, we cannot only zoom into the details. We also need to see the large-scale features from afar. One way to take a step back and get the whole picture is to model the systems as a network. However, many…
We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase…
A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase…
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to…
There is a pressing need for a description of complex systems that includes considerations of the underlying network of interactions, for a diverse range of biological, technological and other networks. In this work relationships between…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…
A general model for the fragmentation of a two-component system (e.g. protons and neutrons) is proposed and solved exactly. The extension of this model to any number of components is also shown to be exactly solvable. A connection between…
Lattice models exhibit significant potential in investigating phase transitions, yet they encounter numerous computational challenges. To address these issues, this study introduces a Monte Carlo-based approach that transforms lattice…
We develop here a simple yet versatile model for nuclear fragmentation in heavy ion collisions. The model allows us to calculate thermodynamic properties such as phase transitions as well as the distribution of fragments at disassembly. In…
In this chapter we present an overview of the main ideas and methods in the fractional integration and cointegration literature. We do not attempt to give a complete survey of this enormous literature, but rather a more introductory…