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

The finite size scaling behaviour for the Ising model in five dimensions,with either free or cyclic boundary, has been the subject for a long runningdebate. The older papers have been based on ideas from e.g. field theory orrenormalization. In this paper we propose a detailed and exact scaling picturefor critical region of the model with cyclic boundary. Unlike the previouspapers our approach is based on a comparison with the existing exact andrigorous results for the FK-random-cluster model on a complete graph. Based onthose results we identify several distinct scaling regions in an $L$-dependentwindow around the critical point. We test these predictions by comparing withdata from Monte Carlo simulations and find a good agreement. The main featurewhich differs between the complete graph and the five dimensional model withfree boundary is the existence of a bimodal energy distribution near thecritical point in the latter. This feature was found by the same authors in anearlier paper in the form of a quasi-first order phase transition for the sameIsing model.

Complete graph asymptotics for the Ising and random cluster models on 5D grids with cyclic boundary