Related papers: Topology and Phase Transitions: Theorem on a neces…
Interacting fermionic ladders are important platforms to study quantum phases of matter, such as different types of Mott insulators. In particular, the D-Mott and S-Mott states hold pre-formed fermion pairs and become paired-fermion liquids…
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…
The study of critical phenomena and phase transitions is an important part of modern condensed matter physics. In this regard, the phenomenological Landau theory has been extraordinarily useful. Hereby we present an alternative theoretical…
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…
The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can further the study of quantum logic and give rise to new…
The topological hypothesis claims that phase transitions in a classical statistical mechanical system are related to changes in the topology of the level sets of the Hamiltonian. So far, the study of this hypothesis has been restricted to…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…
The subject of topological defects has become a very attractive field of study given its apparent relevance to as diverse systems as the early universe and condensed matter. As usually envisaged the topology of the manifold M of the minima…
The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
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…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
Convergence theory is an extension of general topology. In contrast with topology, it is closed under some important operations, like exponentiation. With all its advantages, convergence theory remains rather unknown. It is an aim of this…
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…
The existence of the linear on the order parameter term of the thermodynamic functions expansion near the critical point is justified. The criticism of the arguments, used for the rejection of the odd-power expansion terms of the…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
This is a technical report, containing all the theorem proofs and additional evaluations in paper "Network Capability in Localizing Node Failures via End-to-end Path Measurements" by Liang Ma, Ting He, Ananthram Swami, Don Towsley, and Kin…
Based on the study of saddle points of the potential energy landscapes of generic classical many-particle systems, we present a necessary criterion for the occurrence of a thermodynamic phase transition. Remarkably, this criterion imposes…