相关论文: Phase Transitions on Nonamenable Graphs
Phase transitions are studied in $M$-theory and $F$-theory. In $M$-theory compactification to five dimensions on a Calabi-Yau, there are topology-changing transitions similar to those seen in conformal field theory, but the non-geometrical…
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
This is a status report on a companion subject to extremal combinatorics, obtained by replacing extremality properties with emergent structure, `phases'. We discuss phases, and phase transitions, in large graphs and large permutations,…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
Dynamical equations that are valid in the vicinity of the phase transition into the superconducting state are given. Probable effects of the field of charge carriers' magnetic interactions and the field of temperature fluctuations were…
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the…
We provide a phenomenological theory for topological transitions in restructuring networks. In this statistical mechanical approach energy is assigned to the different network topologies and temperature is used as a quantity referring to…
Phase transitions between two competing vacua of a given theory are quite common in physics. We discuss how to construct the space-time solutions that allow the description of phase transitions between different branches (or asymptotics) of…
Non-equilibrium phase transitions of a scalar field in an expanding spacetime are discussed. These transitions are shown to lead, for appropriate potential energy functions, to a biased choice of vacuum structure which can be analytically…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
A selected set of topics in quantum phase transition is discussed. It includes dissipative quantum phase transitions, the role of disorder, and the relevance of quantum phase transition to measurement theory in quantum mechanics.
A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither…
These notes cover one of the topics programmed for the St Petersburg School in Probability and Statistical Physics of June 2012. The aim is to review recent mathematical developments in the field of random walks in random environment. Our…
In these notes, the application of Feynman's sum-over-paths approach to thermal phase transitions is discussed. The paradigm of such a spacetime approach to critical phenomena is provided by the high-temperature expansion of spin models.…
We consider the multifractal analysis of the pointwise dimension for Gibbs measures on countable Markov shifts. Our paper analyses the set of non-analytic points or phase transitions of the multifractal spectrum. By Sarig's thermodynamic…
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of…
Transition graphs capture the memory and sequential response of multistable media, by specifying their evolution under external driving. Microscopically, collections of bistable elements, or hysterons, provide a powerful model for these…
Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with…