Related papers: Topological properties of the mean field phi^4 mod…
We investigate the potential energy surface of a phi^4 model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_- = 1,…
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…
The stationary points of the potential energy function V are studied for the \phi^4 model on a two-dimensional square lattice with nearest-neighbor interactions. On the basis of analytical and numerical results, we explore the relation of…
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…
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…
We numerically investigate the supercooled dynamics of two simple model liquids exploiting the partition of the multi-dimension configuration space in basins of attraction of the stationary points (inherent saddles) of the potential energy…
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…
By means of molecular dynamics simulations, we study the stationary points of the potential energy in a Lennard-Jones liquid, giving a purely geometric characterization of the energy landscape of the system. We find a linear relation…
We investigate a classical lattice system with $N$ particles. The potential energy $V$ of the scalar displacements is chosen as a $\phi ^4$ on-site potential plus interactions. Its stationary points are solutions of a coupled set of…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
Recent numerical developments in the study of glassy systems have shown that it is possible to give a purely geometric interpretation of the dynamic glass transition by considering the properties of unstable saddle points of the energy.…
The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in…
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…
A topological crystalline insulator (TCI) is a new phase of topological matter, which is predicted to exhibit distinct topological quantum phenomena, since space group symmetries replace the role of time-reversal symmetry in the…
We use the saddle-approach, recently introduced in the numerical investigation of simple model liquids, in the analysis of a mean-field solvable system. The investigated system is the k-trigonometric model, a k-body interaction mean field…
The thermodynamic and kinetic anomalies of supercooled liquids are analyzed from the perspective of energy landscapes. A mean field model, a generalized random energy model of liquids is developed, which exhibits a dynamical transition 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…
A large deviation technique is applied to the mean-field phi4-model, providing an exact expression for the configurational entropy s(v,m) as a function of the potential energy v and the magnetization m. Although a continuous phase…
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…
Equilibrium phase transitions may be defined as nonanalytic points of thermodynamic functions, e.g., of the canonical free energy. Given a certain physical system, it is of interest to understand which properties of the system account for…