Related papers: Telescopic Linkages and Topological Approach to Ph…
The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the…
We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory…
The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant…
In this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field $\phi^4$ model with a $\mathbb{Z}_2$ symmetry. Our purpose is discovering, if any, the relation between 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…
The elsewhere surmised topological origin of phase transitions is given here new important evidence through the analytic study of an exactly solvable model for which both topology and thermodynamics are worked out. The model is a mean-field…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
The thermodynamics and topology of mean-field models with 2+k body interaction terms (generalizing XY model) are derived. Focusing on two particular cases (2+4 and 2+6 body interaction terms), a comparison between thermodynamic (phase…
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
We study topology of configuration spaces of planar linkages having one leg of variable length. Such telescopic legs are common in modern robotics where they are used for shock absorbtion and serve a variety of other purposes. Using a Morse…
Geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure $P$ and variable temperature $T$ is proposed. Equilibrium states of a system at zero external field and fixed $P$ and $T$ are…
The nature of phase transitions involving the questions why and how phase transitions take place has not been sufficiently touched in the literature. In contrast, the current attention to certain extent still focus on the description of…
We critically analyze the possibility of finding signatures of a phase transition by looking exclusively at static quantities of statistical systems, like e.g., the topology of potential energy sub-manifolds (PES). This topological…
We address the question of the quantitative relationship between thermodynamic phase transitions and topological changes in the potential energy manifold analyzing two classes of one dimensional models, the Burkhardt solid-on-solid model…
Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called XY-mean field model and by the phi^4 lattice model, respectively. For…
We show that the presence and the location of first order phase transitions in a thermodynamic system can be deduced by the study of the topology of the potential energy function, V(q), without introducing any thermodynamic measure. In…
We study the mean-field BCS-BEC evolution of a uniform Fermi gas on a single-band triangular lattice, and construct its ground-state phase diagrams, showing a wealth of topological quantum phase transitions between gapped and gapless…
We consider the phase transition in a model which consists of a Ginzburg-Landau free energy for superconductors including a Chern-Simons term. The mean field theory of Halperin, Lubensky and Ma [Phys. Rev. Lett. 32, 292 (1974)] is applied…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
The possibility of topological phase transition with or without a magnetic flux trapped in the cells of a class of decorated lattices is explored in details.Using a tight binding Hamiltonian and a real space decimation scheme we…