相关论文: Phase transitions as topology changes in configura…
We present an explicit example of a gauge symmetry breaking phase transition in heterotic models, the dynamics of which are not thermal and can be described in a well controlled manner throughout. The phase transition is driven by 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…
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may…
In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e.…
We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces.…
Topological phase transition is accompanied with a change of topological numbers. It has been believed that the gap closing and the breakdown of the adiabaticity at the transition point is necessary in general. However, the gap closing is…
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…
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…
We consider the analogy between the topological phase transition which occurs as a function of spatial coordinate on a surface of a non-trivial insulator, and the one which occurs in the bulk due to the change of internal parameters (such…
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 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 topological transitions in one dimensional superconductors that can harbor multiple edge Majorana bound states protected by chiral symmetry. The chiral symmetry arises due to the structure of the internal spin degrees of freedom 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…
Topological properties of a periodic condensed matter system are global features of its Brillouin zone (BZ). In contrast, the validity of effective low energy theories is usually limited to the vicinity of a high symmetry point in the BZ.…
The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…
Two mathematical mechanisms, responsible for the generation of a thermodynamic singularity, are individuated. For a class of short-range, confining potentials, a topology change in some family of configuration space submanifolds is the only…
We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical…
Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a…
We discuss here phase transitions in quantum field theory in the context of vacuum realignment through an explicit construction. Vacuum destabilisation may occur through a scalar attaining a nonzero expectation value, or through a…
Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. This approach provides an alternative way of inspecting the…