English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We extend a recent study of susceptible-infected-removed epidemic processeswith long range infection (referred to as I in the following) from1-dimensional lattices to lattices in two dimensions. As in I we use hashing tosimulate very large lattices for which finite size effects can be neglected, inspite of the assumed power law $p({\bf x})\sim |{\bf x}|^{-\sigma-2}$ for theprobability that a site can infect another site a distance vector ${\bf x}$apart. As in I we present detailed results for the critical case, for thesupercritical case with $\sigma = 2$, and for the supercritical case with $0<\sigma < 2$. For the latter we verify the stretched exponential growth of theinfected cluster with time predicted by M. Biskup. For $\sigma=2$ we findgeneric power laws with $\sigma-$dependent exponents in the supercriticalphase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Insteadof diverging exponentially with the distance from the critical point, thecorrelation length increases with an inverse power, as in an ordinary criticalpoint. Finally we study the dependence of the critical exponents on $\sigma$ inthe regime $0<\sigma <2$, and compare with field theoretic predictions. Inparticular we discuss in detail whether the critical behavior for $\sigma$slightly less than 2 is in the short range universality class, as conjecturedrecently by F. Linder {\it et al.}. As in I we also consider a modified versionof the model where only some of the contacts are long range, the others beingbetween nearest neighbors. If the number of the latter reaches the percolationthreshold, the critical behavior is changed but the supercritical behaviorstays qualitatively the same.

Two-dimensional SIR epidemics with long range infection