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 functional RG for the random field and random anisotropy O(N)sigma-models is studied to two loop. The ferromagnetic/disordered (F/D)transition fixed point is found to next order in d=4+epsilon for N > N_c(N_c=2.8347408 for random field, N_c=9.44121 for random anisotropy). For N <N_c the lower critical dimension plunges below d=4: we find two fixed points,one describing the quasi-ordered phase, the other is novel and describes theF/D transition. The lower critical dimension can be obtained in an(N_c-N)-expansion. The theory is also analyzed at large N and a glassy regimeis found.Comment: 4 pages, 5 figure

Random-Field Spin Models beyond 1 Loop: A Mechanism for Decreasing the Lower Critical Dimension