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

Recently, it has been shown that, when the dimension of a graph turns out tobe infinite dimensional in a broad sense, the upper critical surface and thecorresponding critical behavior of an arbitrary Ising spin glass model definedover such a graph, can be exactly mapped on the critical surface and behaviorof a non random Ising model. A graph can be infinite dimensional in a strictsense, like the fully connected graph, or in a broad sense, as happens on aBethe lattice and in many random graphs. In this paper, we firstly introduceour definition of dimensionality which is compared to the standard definitionand readily applied to test the infinite dimensionality of a large class ofgraphs which, remarkably enough, includes even graphs where the tree-likeapproximation (or, in other words, the Bethe-Peierls approach), in general, maybe wrong. Then, we derive a detailed proof of the mapping for all the graphssatisfying this condition. As a byproduct, the mapping provides immediately avery general Nishimori law.

journal of statistical mechanics

Ising spin glass models versus Ising models: an effective mapping at  high temperature III. Rigorous formulation and detailed proof for general  graphs