English
Related papers

Related papers: Multicritical behavior of the diluted contact proc…

200 papers

In this work we study the one-dimensional contact process with diffusion using two different approaches to research the critical properties of this model: the supercritical series expansions and finite-size exact solutions. With special…

Statistical Mechanics · Physics 2009-11-13 W. G. Dantas , M. J. de Oliveira , J. F. Stilck

In this paper we will consider the contact process in a very simple type of random environment that physicists call the random dilution model. We start with the contact process on a graph, here either $\mathbb{Z}^d$, a $d$-dimensional torus…

Probability · Mathematics 2025-06-02 Rick Durrett

A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behaviour observed along the transition line…

Statistical Mechanics · Physics 2009-11-10 F. Ginelli , V. Ahlers , R. Livi , D. Mukamel , A. Pikovsky , A. Politi , A. Torcini

We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…

Statistical Mechanics · Physics 2009-04-27 Man Young Lee , Thomas Vojta

We consider the contact process near an extended surface defect, where the local control parameter deviates from the bulk one by an amount of $\lambda(l)-\lambda(\infty) = A l^{-s}$, $l$ being the distance from the surface. We concentrate…

Statistical Mechanics · Physics 2018-01-12 R. Juhász , F. Iglói

I study the absorbing-state phase transition in the one-dimensional contact process with mobile disorder. In this model the dilution sites, though permanently inactive, diffuse freely, exchanging positions with the other sites, which host a…

Statistical Mechanics · Physics 2015-05-13 Ronald Dickman

For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution…

Probability · Mathematics 2011-01-10 J. van den Berg

We consider a dilute lattice obtained from the usual $\mathbb{Z}^3$ lattice by removing independently each of its columns with probability $1-\rho$. In the remaining dilute lattice independent Bernoulli bond percolation with parameter $p$…

Probability · Mathematics 2020-05-01 Marcelo R. Hilário , Marcos Sá , Rémy Sanchis

We consider a contact process on $Z^d$ with two species that interact in a symbiotic manner. Each site can either be vacant or occupied by individuals of species $A$ and/or $B$. Multiple occupancy by the same species at a single site is…

Probability · Mathematics 2019-12-11 Rick Durrett , Dong Yao

Recently, the quantum contact process, in which branching and coagulation processes occur both coherently and incoherently, was theoretically and experimentally investigated in driven open quantum spin systems. In the semi-classical…

Statistical Mechanics · Physics 2020-02-21 Minjae Jo , B. Kahng

We study the contact process on the long-range percolation cluster on $\mathbb{Z}$ where each edge $\langle i,j \rangle$ is open with probability $|i-j|^{-s}$ for $s> 2$. Using a renormalization procedure we apply Peierls-type argument to…

Probability · Mathematics 2026-03-17 Pablo A. Gomes , Marcelo R. Hilário , Bernardo N. B. de Lima , Thomas Mountford

A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails,…

Quantum Gases · Physics 2015-06-19 Y. -Y. Chen , Y. -Z. Jiang , X. -W. Guan , Qi Zhou

The phase transition of the one-dimensional, diffusive pair contact process (PCPD) is investigated by N cluster mean-field approximations and high precision simulations. The N=3,4 cluster approximations exhibit smooth transition line to…

Statistical Mechanics · Physics 2009-11-07 Geza Odor

We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte-Carlo simulations for times up to $10^{10}$ and system sizes up to $8000 \times 8000$ sites. Our…

Disordered Systems and Neural Networks · Physics 2009-01-13 Thomas Vojta , Adam Farquhar , Jason Mast

We study the contact process on spatially embedded networks, consisting of a regular square lattice with long-range connections. To generate the networks, a long-range connection is randomly added to each node $i$ of a square lattice,…

Statistical Mechanics · Physics 2018-09-26 T. B. dos Santos , C. I. N. Sampaio Filho , N. A. M. Araújo , C. L. N. Oliveira , A. A. Moreira

We study the pair contact process with diffusion (PCPD) using Monte Carlo simulations, and concentrate on the decay of the particle density $\rho$ with time, near its critical point, which is assumed to follow $\rho(t) \approx ct^{-\delta}…

Statistical Mechanics · Physics 2012-08-07 R. D. Schram , G. T. Barkema

The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class,…

Statistical Mechanics · Physics 2015-05-27 F. L. Santos , Ronald Dickman , U. L. Fulco

Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…

Statistical Mechanics · Physics 2026-05-26 Qiyuan Shi , Shuo Wei , Youjin Deng , Ming Li

We study a contact process (CP) with two species that interact in a symbiotic manner. In our model, each site of a lattice may be vacant or host individuals of species A and/or B; multiple occupancy by the same species is prohibited.…

Statistical Mechanics · Physics 2012-05-29 Marcelo Martins de Oliveira , Renato Vieira Dos Santos , Ronald Dickman

We study the random connection model on hyperbolic space $\mathbb{H}^d$ in dimension $d=2,3$. Vertices of the spatial random graph are given as a Poisson point process with intensity $\lambda>0$. Upon variation of $\lambda$ there is a…

Probability · Mathematics 2025-10-14 Matthew Dickson , Markus Heydenreich