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 ferromagnetic random-field Ising model on random graphs of fixedconnectivity z (Bethe lattice) in the presence of an external magnetic field$H$. We compute the number of single-spin-flip stable configurations with agiven magnetization m and study the connection between the distribution ofthese metastable states in the H-m plane (focusing on the region where thenumber is exponentially large) and the shape of the saturation hysteresis loopobtained by cycling the field between $-\infty$ and $+\infty$ at T=0. Theannealed complexity $\Sigma_A(m,H)$ is calculated for z=2,3,4 and the quenchedcomplexity $\Sigma_Q(m,H)$ for z=2. We prove explicitly for z=2 that thecontour $\Sigma_Q(m,H)=0$ coincides with the saturation loop. On the otherhand, we show that $\Sigma_A(m,H)$ is irrelevant for describing, evenqualitatively, the observable hysteresis properties of the system.Comment: 22 pages, 10 figures Manuscript revised to clarify a few points.  Final version to appear in EPJ

Metastable states and T=0 hysteresis in the random-field Ising model on random graphs