Related papers: The existence phase transition for two Poisson ran…
In this paper we study the Poisson stick model in two dimensional hyperbolic space $\mathbb{H}^2,$ where the sticks all have length $L.$ Typically, percolation models in hyperbolic space undergo two phase transitions as the intensity…
Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of…
We study cosmological phase transitions from modified equations of motion by introducing two non-commutative parameters in the Poisson brackets, which describes the initial- and future-singularity-free phase transition in the soluble…
An important component in studying mathematical models in many biochemical systems, such as those found in developmental biology, is phase transition. The purpose of this work is to analyze the phase transition property of a…
A fast method is presented for simulating the dielectric-breakdown model using iterated conformal mappings. Numerical results for the dimension and for corrections to scaling are in good agreement with the recent RG prediction of an upper…
In the framework of the interacting boson model the three transitional regions (rotational-vibrational, rotational-$\gamma$-unstable and, vibrational-$\gamma$-unstable transitions) are reanalyzed. A new kind of plot is presented for…
We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
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…
In this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd\H{o}s-R\'{e}nyi networks, scale-free networks, and…
Dynamical quantum phase transitions occur when a dynamical free energy becomes non-analytic at critical \emph{times}. They have been shown to exist in, among other systems, topological insulators and superconductors. Additionally in both…
We study the criticality of a Potts interface by introducing a {\it froth} model which, unlike its SOS Ising counterpart, incorporates bubbles of different phases. The interface is fractal at the phase transition of a pure system. However,…
We consider a slight modification of the frog model. For a given graph, each vertex has $\mathrm{Poisson}(\lambda)$ particles (or frogs). At time zero, only the particles at the origin are active, and all the other particles are sleeping.…
We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with…
We study the 2d-Ising model defined on finite boxes at temperatures that are below but very close from the critical point. When the temperature approaches the critical point and the size of the box grows fast enough, we establish large…
We study the total variation (TV) distance between the laws of the 2D Ising/FK-Ising model in a box of side-length $N$ with and without an i.i.d.\ Gaussian external field with variance $\epsilon^2$. Letting the external field strength…
We investigate a spatial random graph model whose vertices are given as a marked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pair of points independently with probability depending on the spatial displacement of the…
We study a statistical mechanics model of two species of bosons with mutual statistics $\theta=2\pi/n$ in (2+1) dimensions. This model realizes a fractionalized topological phase of bosons, which is a fractionalized version of the boson…
Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any…
We re-examine a population model which exhibits a continuous absorbing phase transition which belongs to directed percolation in 1+1 dimensions and a first order transition in 2+1 dimensions and above. Studying the model on fractal…