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The one-dimensional kinetic contact process with parallel update is introduced and studied by the mean-field approximation and Monte Carlo (MC) simulations. Contrary to a more conventional scenario with single active phase for 1d models…

Statistical Mechanics · Physics 2015-03-17 P. N. Timonin , G. Y. Chitov

Kinetically constrained models (KCMs) are interacting particle systems introduced in the '80s by physicists to have accessible stochastic models with glassy-type dynamics. The key mechanism behind the complex evolution of these otherwise…

Probability · Mathematics 2025-10-24 Fabio Martinelli , Assaf Shapira , Cristina Toninelli

The bisection method for kinetically constrained models (KCM) of Cancrini, Martinelli, Roberto and Toninelli is a vital technique applied also beyond KCM. In this note we present a new way of performing it, based on a novel two-block…

Probability · Mathematics 2021-12-07 Ivailo Hartarsky

Two-dimensional bootstrap percolation is a cellular automaton in which sites become 'infected' by contact with two or more already infected nearest neighbors. We consider these dynamics, which can be interpreted as a monotone version of the…

Probability · Mathematics 2010-12-27 Janko Gravner , Alexander E. Holroyd , Robert Morris

In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper…

Probability · Mathematics 2023-08-22 Paul Balister , Béla Bollobás , Robert Morris , Paul Smith

$k$-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analysing the resilience of a network under random damage, an extension of this model is introduced,…

Disordered Systems and Neural Networks · Physics 2013-02-22 Davide Cellai , Aonghus Lawlor , Kenneth A. Dawson , James P. Gleeson

We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple…

Disordered Systems and Neural Networks · Physics 2009-11-07 Frank O. Pfeiffer , Heiko Rieger

We analyze critical points that can be induced in glassy systems by the presence of constraints. These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in…

Statistical Mechanics · Physics 2014-04-01 Silvio Franz , Giorgio Parisi

We study the set of possible configurations for a general kinetically constrained model (KCM), a non monotone version of the $\mathcal{U}$-bootstrap percolation cellular automata. We solve a combinatorial question that is a generalization…

Probability · Mathematics 2020-06-24 Laure Marêché

We study the boundary critical behavior of the three-dimensional Heisenberg universality class, in the presence of a bidimensional surface. By means of high-precision Monte Carlo simulations of an improved lattice model, where leading bulk…

Statistical Mechanics · Physics 2025-05-12 Francesco Parisen Toldin

Consider a $p$-random subset $A$ of initially infected vertices in the discrete cube $[L]^3$, and assume that the neighbourhood of each vertex consists of the $a_i$ nearest neighbours in the $\pm e_i$-directions for each $i \in \{1,2,3\}$,…

Probability · Mathematics 2019-09-02 Daniel Blanquicett

Majority bootstrap percolation is a model of infection spreading in networks. Starting with a set of initially infected vertices, new vertices become infected once half of their neighbours are infected. Balogh, Bollob\'{a}s and Morris…

Combinatorics · Mathematics 2025-07-10 Maurício Collares , Joshua Erde , Anna Geisler , Mihyun Kang

We consider the Constrained-degree percolation model on the hypercubic lattice, $\mathbb L^d=(\mathbb Z^d,\mathbb E^d)$ for $d\geq 3$. It is a continuous time percolation model defined by a sequence, $(U_e)_{e\in\mathbb E^d}$, of i.i.d.…

Probability · Mathematics 2023-01-03 Ivailo Hartarsky , Bernardo N. B. de Lima

Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the…

Probability · Mathematics 2012-10-04 Nicoletta Cancrini , Fabio Martinelli , Cyril Roberto , Cristina Toninelli

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 FA-jf and on an oriented version of them. These tree models…

Probability · Mathematics 2013-09-12 F. Martinelli , C. Toninelli

Kinetically constrained models (KCM) are systems with trivial thermodynamics but often complex dynamical behavior due to constraints on the accessible paths followed by the system. Exploring these properties, the Kob-Andersen (KA) model was…

Soft Condensed Matter · Physics 2010-05-12 Jeferson J. Arenzon

The critical behavior of the contact process (CP) in heterogeneous periodic and weakly-disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical…

Statistical Mechanics · Physics 2009-11-11 C. J. Neugebauer , S. V. Fallert , S. N. Taraskin

We investigate aspects of universality of Glauber critical dynamics in two dimensions. We compute the critical exponent $z$ and numerically corroborate its universality for three different models in the static Ising universality class and…

Statistical Mechanics · Physics 2009-10-31 M. P. Nightingale , H. W. J. Bloete

Tensor models generalize the matrix-model approach to 2-dimensional quantum gravity to higher dimensions. Some models allowing a $1/N$ expansion have been explored, most of them generating branched-polymer geometries. Recently, enhancements…

High Energy Physics - Theory · Physics 2019-03-15 Luca Lionni , Johannes Thürigen

In this paper we study monotone cellular automata in $d$ dimensions. We develop a general method for bounding the growth of the infected set when the initial configuration is chosen randomly, and then use this method to prove a lower bound…

Probability · Mathematics 2022-11-08 Paul Balister , Béla Bollobás , Robert Morris , Paul Smith