The survival of large dimensional threshold contact processes (2009)
Mountford, Thomas, Schonmann, Roberto H.
We study the threshold $\theta$ contact process on $\mathbb{Z}^d$ with infection parameter $\lambda$. We show that the critical point $\lambda_{\mathrm{c}}$, defined as the threshold for survival...
Metastable behavior for bootstrap percolation on regular trees (2009)
Biskup, Marek, Schonmann, Roberto H.
We examine bootstrap percolation on a regular (b+1)-ary tree with initial law given by Bernoulli(p). The sites are updated according to the usual rule: a vacant site becomes occupied if it has at...
Facilitated oriented spin models:some non equilibrium results (2008)
Cancrini, Nicoletta, Martinelli, Fabio, Schonmann, Roberto H., Toninelli, Cristina
We analyze the relaxation to equilibrium for kinetically constrained spin models (KCSM) when the initial distribution $\nu$ is different from the reversible one, $\mu$. This setting has been...
The Ising Model on Diluted Graphs and Strong Amenability (2007)
Roberto H. Schonmann, Jeffrey E. Steif
Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external field. We show that...
Percolation in ∞+1 Dimensions at the Uniqueness Threshold (2007)
: For independent density p site percolation on the (transitive non-amenable) graph T b \Theta Z, where T b is a homogeneous tree of degree b + 1, and b is supposed to be large, it is shown that for...
A Note on Percolation in a Voronoi Competition-Growth Model (2007)
Elisabeti Kira, E. Jordão Neves, E. Jord~ao Neves, Roberto H. Schonmann
We study a model in which two entities (e.g., plant species, political ideas, ...) compete for space on a plane, starting from randomly distributed seeds, and growing deterministically at possibly...
EINSTEIN RELATION FOR A CLASS OF INTERFACE MODELS (2007)
ABSTRACT. A class of SOS interface models which can be seen as simplified stochastic Ising model interfaces is studied. In the absence of an external field the long-time fluctuations of the interface...
Threshold $theta geq 2$ contact processes on homogeneous trees (2006)
Fontes, Luiz Renato, Schonmann, Roberto H.
We study the threshold $theta geq 2$ contact process on a homogeneous tree $T_b$ of degree $kappa = b + 1$, with infection parameter $lambda geq 0$ and started from a product measure with density...
3D crystal: how flat its flat facets are? (2004)
Bodineau, Thierry, Schonmann, Roberto H., Shlosman, Senya
We investigate the hypothesis that the (random) crystal of the $(-)$-phase inside the $(+)$-phase of the 3D canonical Ising model has flat facets. We argue that it might need to be weakened, due to...
Mixed percolation as a bridge between site and bond percolation (2000)
Chayes, Lincoln, Schonmann, Roberto H.
By using mixed percolation as a bridge between site and bond percolation, we derive a new inequality between the critical points of these processes that is optimal in a certain sense.We also extend a...
The Ising model on diluted graphs and strong amenability (2000)
Häggström, Olle, Schonmann, Roberto H., Steif, Jeffrey E.
Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external field.We show that...
Multiplicity Of Phase Transitions And Mean-Field Criticality On Highly Non-Amenable Graphs (2000)
. We consider independent percolation, Potts (especially Ising) models and the contact process on innite, locally nite, connected graphs, with emphasis on transitive graphs. The presence of more than...
The Second Lowest Extremal Invariant Measure of the Contact Process II (1999)
Salzano, Marcia, Schonmann, Roberto H.
We continue the investigation of the behavior of the contact process on infinite connected graphs of bounded degree. Some questions left open by Salzano and Schonmann (1997) concerning the notions of...
The Ising Model on Diluted Graphs and Strong Amenability (1999)
Olle Häggström, Roberto H. Schonmann, Jeffrey E. Steif
Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external eld. We show that for...
The Ising Model on Diluted Graphs and Strong Amenability (1999)
Olle Häggström, Roberto H. Schonmann, Jeffrey E. Steif
Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external field. We show that...
Salzano, Marcia, Schonmann, Roberto H.
We provide a new proof, substantially simpler than Zhang’s original one, that for the contact process on homogeneous trees, local survival implies complete convergence.
Lack of monotonicity in ferromagnetic Ising model phase diagrams (1998)
Schonmann, Roberto H., Tanaka, Nelson I.
We study patterns of the phase diagram of ferromagnetic Ising models on graphs under an external magnetic field. We provide an example of a tree with only two types of vertices on which for a range...
The Griffiths Singularity Random Field (1998)
Aernout Van Enter, The Netherl, Christian Maes, Inst Theoretische, Inst Theoretische, ...
We consider a spin system on sites of a d-dimensional cubic lattice (d 2), with the values 0; 1 or \Gamma1. It is built over the Bernoulli site percolation model, with spins taking the value 0 on...
Dobrushin-Kotecky-Shlosman Theorem Up To The Critical Temperature (1998)
ROBERTO H. SCHONMANN, Dmitry Ioffe, Dmitry Ioffe, Roberto H. Schonmann
. We develop a non-perturbative version of the Dobrushin-Koteck'y-Shlosman theory of phase separation in the canonical 2D Ising ensemble. The results are valid for all temperatures below...
The second lowest extremal invariant measure of the contact process (1997)
Salzano, Marcia, Schonmann, Roberto H.
We study the ergodic behavior of the contact process on infinite connected graphs of bounded degree. We show that the fundamental notion of complete convergence is not as well behaved as it was...
Complete Analyticity Of The 2D Potts Model Above The Critical Temperature (1997)
Roberto Fernández, Roberto Fern Andez, Roberto H. Schonmann, Senya B. Shlosman
. We investigate the complete analyticity (CA) of the two-dimensional q- state Potts model for large values of q. We are able to prove it for every temperature T ? Tcr (q), provided we restrict...
Equivalence of exponential decay rates for bootstrap percolation like cellular automata (1995)
Andjel, Enrique D., Mountford, Thomas S., Schonmann, Roberto H.
On Some Growth Models With A Small Parameter (1995)
Harry Kesten, Roberto H. Schonmann
. We consider the behavior of the asymptotic speed of growth and the asymptotic shape in some growth models, when a certain parameter becomes small. The basic example treated is the variant of...