Related papers: On the relationship between phase transitions and …
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…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…
One-dimensional thermodynamic instabilities are phase transitions not prohibited by Landau's argument, because the energy of the domain wall (DW) which separates the two phases is infinite. Whether they actually occur in a given system of…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
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…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
We demonstrate the existence of topological phase transitions in interacting, symmetry-protected quantum matter at finite temperatures. Using a combined numerical and analytical approach, we study a one-dimensional Su-Schrieffer-Heeger…
For physical systems described by smooth, finite-range and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that unless the equipotential…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
There are various methods for modeling phase transformations in materials science, including general classes of phase-field methods and reactive diffusion methodologies, which most importantly differ in their treatment of interface energy.…
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…
We consider the links between nonlinear dynamics and thermodynamics in the framework of a simple nonlinear model for DNA. Two analyses of the phase transition, either with the transfer integral approach or by considering the instability of…
Various phase transitions in models for coupled charge-density waves are investigated by means of the $\epsilon$-expansion, mean-field theory, and Monte Carlo simulations. At zero temperature the effective action for the system with…
We propose a relationship between thermodynamic phase transitions and ground-state quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex…
We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of…
A topological approach to the theory of equilibrium phase transitions in statistical physics is based on the Topological Hypothesis (TH), which claims that phase transitions are due to changes of the topology of suitable submanifolds in the…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
We show that thermodynamics can be formulated naturally from the intrinsic geometry of phase space alone-without postulating an ensemble, which instead emerges from the geometric structure itself. Within this formulation, phase transitions…
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 study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology and energetics, we show that for a generic normal state band…