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 local Yang-Baxter equation (YBE), introduced by Maillet and Nijhoff, is aproper generalization to 3 dimensions of the zero curvature relation. Recently,Korepanov has constructed an infinite set of integrable 3-dimensional latticemodels, and has related them to solutions to the local YBE. The simplestKorepanov's model is related to the star-triangle relation in the Ising model.In this paper the corresponding discrete equation is derived. In the continuouslimit it leads to a differential 3d equation, which is symmetric with respectto all permutations of the three coordinates. A similar analysis of thestar-triangle transformation in electric networks leads to the discretebilinear equation of Miwa, associated with the BKP hierarchy. Some relatedoperator solutions to the tetrahedron equation are also constructed.Comment: 10 pages, LaTeX, no figure

On discrete three-dimensional equations associated with the local Yang-Baxter relation