Related papers: Percolation Transition in a Topological Phase
Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the…
Topological order is defined by topological invariants, rather than symmetries and local order parameters. Nonetheless some topological phases can be characterized by string order parameters and entanglement. In this article we study how…
Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, e.g. it can bend without…
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 the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems,…
Higher-form symmetries are a valuable tool for classifying topological phases of matter. However, emergent higher-form symmetries in interacting many-body quantum systems are not typically exact due to the presence of topological defects.…
The possible paralelism existing between phase transitions and fracture in disordered materials, is discussed using the well-known Fiber Bundle Models and a probabilistic approach suited to smooth fluctuations near the critical point. Two…
The ground states of noninteracting fermions in one-dimension with chiral symmetry form a class of topological band insulators, described by a topological invariant that can be related to the Zak phase. Recently, a generalization of this…
Clustering $\unicode{x2013}$ the tendency for neighbors of nodes to be connected $\unicode{x2013}$ quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase…
Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated…
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be…
A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
A hallmark of topological phases is the occurrence of topologically protected modes at the system`s boundary. Here we find topological phases in the antisymmetric Lotka-Volterra equation (ALVE). The ALVE is a nonlinear dynamical system and…
In the present paper, the connection between surface order-disorder phase transitions and the percolating properties of the adsorbed phase has been studied. For this purpose, four lattice-gas models in presence of repulsive interactions…
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the…
The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin…