Related papers: Topological regulation of activation barriers on f…
We study a free fermion model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases of distinct topological order. We show the presence of a topological phase transition that is of a…
We investigate the time dependent Ginzburg-Landau (TDGL) equation for a non conserved order parameter on an infinitely ramified (deterministic) fractal lattice employing two alternative methods: the auxiliary field approach and a numerical…
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological…
Exponential growth describes an extremely rapid process ubiquitous across mathematics and diverse physical, biological, and technological systems. Here, we introduce a class of fractal-inspired lattices that combine long-range periodic…
Quantum systems with short range interactions are known to respect an area law for the entanglement entropy: the von Neumann entropy $S$ associated to a bipartition scales with the boundary $p$ between the two parts. Here we study the case…
We study the dynamics of phase ordering of a non-conserved, scalar order parameter in one dimension, with long-range interactions characterized by a power law $r^{-d-\sigma}$. In contrast to higher dimensional systems, the point nature of…
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…
Dynamical quantum systems both driven by unitary evolutions and monitored through measurements have proved to be fertile ground for exploring new dynamical quantum matters. While the entanglement structure and symmetry properties of…
The dynamics of Boolean networks (the N-K model) with scale-free topology are studied here. The existence of a phase transition governed by the value of the scale-free exponent of the network is shown analytically by analyzing the overlap…
We analyse a model of fixed in-degree Random Boolean Networks in which the fraction of input-receiving nodes is controlled by a parameter gamma. We investigate analytically and numerically the dynamics of graphs under a parallel XOR…
In interacting topological systems, Landau-like order parameters interplay with the band topology of fermions. The physics of domain formation in such systems can get significantly altered due to the presence of topological fermions. In…
The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws.…
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 investigate the higher-order connectivity of scale-free networks using algebraic topology. We model scale-free networks as preferential attachment graphs, and we study the algebraic-topological properties of their clique complexes. We…
Temporal gene expression data (Wen, et. al.) was analyzed using the recently introduced inverse modeling technique of Embedded Complex Logistic Maps (ECLM). Preliminary results indicate scale-free structure in the gene regulatory network…
This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II…
The statics and dynamics of a surface separating two phases of a relativistic quantum field theory at or near the critical temperature typically make use of a free energy as a functional of an order parameter. This free energy functional…
The research on topological phenomena in ferroelectric materials has revolutionized the way we understand polar order. Intriguing examples are polar skyrmions, vortex/anti-vortex structures and ferroelectric incommensurabilties, which…
We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified…
Self-organization to ferromagnetic phase transition in cellular automata of spins governed by stochastic majority rule and when topology between spins is changed, is investigated numerically. Three types of edge rewiring are considered. The…