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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the scaling limit of subcritical long-range Ising models with(super)-summable interactions on $\mathbb{Z}^d$. We show that for a wide classof models, the scaling limit is white noise. In the specific case of couplings$J_{x,y}=|x-y|^{-d-\boldsymbol{\alpha}}$, where $\boldsymbol{\alpha}>0$ and$|\cdot|$ is the Euclidean norm, we find an emergence of fractional Gaussianfree field correlations in appropriately renormalised and rescaled observables.The proof exploits exact asymptotics of the two-point function, firstestablished by Newman and Spohn (1998), together with the rotational symmetryof the interaction.

Emergence of fractional Gaussian free field correlations in subcritical long-range Ising models