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 loop $O(n)$ model on the honeycomb lattice. By means of localnon-planar deformations of the lattice, we construct a discrete stress-energytensor. For $n\in [-2,2]$, it gives a new observable satisfying a part ofCauchy-Riemann equations. We conjecture that it is approximatelydiscrete-holomorphic and converges to the stress-energy tensor in thecontinuum, which is known to be a holomorphic function with the Schwarzianconformal covariance. In support of this conjecture, we prove it for the caseof $n=1$ which corresponds to the Ising model. Moreover, in this case, we showthat the correlations of the discrete stress-energy tensor with primary fieldsconverge to their continuous counterparts, which satisfy the OPEs given by theCFT with central charge $c=1/2$.  Proving the conjecture for other values of $n$ remains a challenge. Inparticular, this would open a road to establishing the convergence of theinterface to the corresponding $\mathrm{SLE}_\kappa$ in the scaling limit.

Discrete stress-energy tensor in the loop O(n) model