Threshold-limited spreading in social networks with multiple initiators

P Singh, S Sreenivasan, BK Szymanski, G Korniss - Scientific reports, 2013‏ - nature.com
A classical model for social-influence-driven opinion change is the threshold model. Here
we study cascades of opinion change driven by threshold model dynamics in the case …

Bootstrap percolation on homogeneous trees has 2 phase transitions

LRG Fontes, RH Schonmann - Journal of Statistical Physics, 2008‏ - Springer
We study the threshold θ bootstrap percolation model on the homogeneous tree with degree
b+ 1, 2≤ θ≤ b, and initial density p. It is known that there exists a nontrivial critical value for …

Phase transitions in probabilistic cellular automata

L Ponselet - arxiv preprint arxiv:1312.3612, 2013‏ - arxiv.org
We investigate the low-noise regime of a large class of probabilistic cellular automata,
including the North-East-Center model of A. Toom. They are defined as stochastic …

[HTML][HTML] A first order phase transition in the threshold θ≥ 2 contact process on random r-regular graphs and r-trees

S Chatterjee, R Durrett - Stochastic Processes and their Applications, 2013‏ - Elsevier
We consider the discrete time threshold-θ contact process on a random r-regular graph. We
show that if θ≥ 2, r≥ θ+ 2, ϵ1 is small and p≥ p1 (ϵ1), then starting from all vertices …

Kinetically constrained spin models on trees

F Martinelli, C Toninelli - 2013‏ - projecteuclid.org
We analyze kinetically constrained 0–1 spin models (KCSM) on rooted and unrooted trees
of finite connectivity. We focus in particular on the class of Friedrickson–Andersen models …

Critical discontinuous phase transition in the threshold contact process

EF da Silva, MJ de Oliveira - Journal of Physics A: Mathematical …, 2011‏ - iopscience.iop.org
We analyze a threshold contact process on a square lattice in which particles are created on
empty sites with at least two neighboring particles and are annihilated spontaneously. We …

[HTML][HTML] Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

CJ Wang, DJ Liu, JW Evans - The Journal of Chemical Physics, 2015‏ - pubs.aip.org
Threshold versions of Schloegl's model on a lattice, which involve autocatalytic creation and
spontaneous annihilation of particles, can provide a simple prototype for discontinuous non …

Discontinuous Phase Transitions in Nonlocal Schloegl Models for Autocatalysis: Loss and Reemergence of a Nonequilibrium Gibbs Phase Rule

DJ Liu, CJ Wang, JW Evans - Physical Review Letters, 2018‏ - APS
We consider Schloegl models (or contact processes) where particles on a square grid
annihilate at a rate p and are created at a rate of kn= n (n− 1)/[N (N− 1)] at empty sites with n …

Phase transitions in Schloegl's second model for autocatalysis on a Bethe lattice

DJ Liu, CJ Wang, JW Evans - Physical Review E, 2021‏ - APS
Schloegl's second model (also known as the quadratic contact process) on a lattice involves
spontaneous particle annihilation at rate p and autocatalytic particle creation at empty sites …

The survival of large dimensional threshold contact processes

T Mountford, RH Schonmann - 2009‏ - projecteuclid.org
We study the threshold θ contact process on ℤ d with infection parameter λ. We show that
the critical point λ c, defined as the threshold for survival starting from every site occupied …