Related papers: A geometric conjecture about phase transitions
Thermodynamic conventions suffer from describing dynamical distinctions, especially when the structural and energetic changes induced by localized rare events are insignificant. By using the ensemble theory in the trajectory space, we…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
In contrast to ordinary symmetries, supersymmetry interchanges bosons and fermions. Originally proposed as a symmetry of our universe, it still awaits experimental verification. Here we theoretically show that supersymmetry emerges…
The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
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…
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with…
In a system of many similar self-propelled entities such as flocks of birds, fish school, cells and molecules, the interactions with neighbors can lead to a "coherent state", meaning the formation of visually compelling aggregation patterns…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting liquid and crystal phases.…
In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
We review recent developments in structural-dynamical phase transitions in trajectory space. An open question is how the dynamic facilitation theory of the glass transition may be reconciled with thermodynamic theories that posit a…
It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase…
The traditional concept of phase transitions has, in recent years, been widened in a number of interesting ways. The concept of a topological phase transition separating phases with a different ground state topology, rather than phases of…
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…
Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres,…
We propose a definition of phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. This generalizes all the definitions based on the curvature anomalies of thermodynamical…