Related papers: The sandpile model on the complete split graph: $q…
The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice $\mathbb{Z}^d$, in which sites with at least 2d chips {\em topple}, distributing 1 chip to each of their…
We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the…
A sandpile is a cellular automaton on a graph that evolves by the following toppling rule: if the number of grains at a vertex is at least its valency, then this vertex sends one grain to each of its neighbors. In the study of pattern…
It is commonly believed that models defined on a closed one-dimensional manifold cannot give rise to topological order. Here we construct frustration-free Hamiltonians which possess both symmetry protected topological order (SPT) on the…
We introduce and study numerically a directed two-dimensional sandpile automaton with probabilistic toppling (probability parameter p) which provides a good laboratory to study both self-organized criticality and the far-from-equilibrium…
We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of…
We unveil the microscopic origin of the topologically ordered counterpart of the s-wave superconductor in this work. For this, we employ the recently developed unitary renormalisation group (URG) method on a generalised model of 2D…
We classify all recurrent configurations of the Abelian sandpile model (ASM) on Ferrers graphs. The classification is in terms of decorations of EW-tableaux, which undecorated are in bijection with the minimal recurrent configurations. We…
We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral…
Abramovich, Corti and Vistoli have studied modular compactifications of stacks of curves equipped with abelian level structures arising as substacks of the stack of twisted stable maps into the classifying stack of a finite group, provided…
The Abelian Sandpile Model is a discrete diffusion process defined on graphs (Dhar \cite{DD90}, Dhar et al. \cite{DD95}) which serves as the standard model of self-organized criticality. The transience class of a sandpile is defined as the…
The height probabilities for the recurrent configurations in the Abelian Sandpile Model on the square lattice have analytic expressions, in terms of multidimensional quadratures. At first, these quantities have been evaluated numerically…
We introduce a new model of a stochastic sandpile on a graph $G$ containing a sink. When unstable, a site sends one grain to each of its neighbours independently with probability $p \in (0,1]$. For $p=1$, this coincides with the standard…
The Abelian Sandpile Model, seen as a deterministic lattice automaton, on two-dimensional periodic graphs generates complex regular patterns displaying (fractal) self-similarity. In particular, on a variety of lattices and initial…
The first part of this paper ( arXiv:1607.02114 ) introduced splitting trees, those chronological trees admitting the self-similarity property where individuals give birth, at constant rate, to iid copies of themselves. It also established…
Topological crystalline insulators (TCI) are insulating electronic phases of matter with nontrivial topology originating from crystalline symmetries. Recent theoretical advances have provided powerful guidelines to search for TCIs in real…
Using the theory of Dirichlet forms we construct a large class of continuous semimartingales on an open domain $E \subset \mathbb{R}^d$, which are governed by rank-based, in addition to name-based, characteristics. Using the results of Baur…
We study the abelian sandpile model on decorated one dimensional chains. We determine the structure and the asymptotic form of distribution of avalanche-sizes in these models, and show that these differ qualitatively from the behavior on a…
Abelian sandpile models, both deterministic, such as the Bak, Tang, Wiesenfeld (BTW) model [P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. {\bf 59}, 381 (1987)], and stochastic, such as the Manna model [S.S. Manna, J. Phys. A {\bf 24},…
We consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between…