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

In this paper, we investigate the finite connectivity spin-glass problem. Ourwork is focused on the expansion around the point of infinite connectivity ofthe free energy of a spin glass on a graph with Poissonian distributedconnectivity: we are interested to study the first-order correction to theinfinite connectivity result for large values or the connectivity $z$. The samecalculations for one and two replica symmetry breakings were done in previousworks; the result for the first-order correction was divergent in the limit ofzero temperature and it was suggested that it was an artifact for having afinite number of replica symmetry breakings. In this paper we are able tocalculate the expansion for an infinite number of replica symmetry breakings:in the zero-temperature limit, we obtain a well defined free energy. We haveshown that cancellations of divergent terms occur in the case of an infinitenumber of replica symmetry breakings and that the pathological behavior of theexpansion was due only to the finite number of replica symmetry breakings.

Free energy expansion of the spin glass with finite connectivity for $\infty$ RSB