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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Using the planar Temperley-Lieb algebra, critical bond percolation on thesquare lattice is incorporated as ${\cal LM}(2,3)$ in the family of Yang-Baxterintegrable logarithmic minimal models ${\cal LM}(p,p')$. We consider this modelin the presence of boundaries and with periodic boundary conditions. Inspiredby Kuniba, Sakai and Suzuki, we rewrite the recently obtained infinite$Y$-system of functional equations. We obtain nonlinear integral equations inthe form of a closed finite set of TBA equations described by a $D_3$ Dynkindiagram. Following the methods of Kl\"umper and Pearce, we solve the TBAequations for the conformal finite-size corrections. For the ground states ofthe standard modules on the strip, these agree with the known central charge$c=0$ and conformal weights $\Delta_{1,s}$ for $s\in {\Bbb Z_{\ge 1}}$ with$\Delta_{r,s}= \big((3r-2s)^2-1\big)/24$. For the periodic case, thefinite-size corrections agree with the conformal weights $\Delta_{0,s}$,$\Delta_{1,s}$ with $s\in\frac12\Bbb Z_{\ge0}$. These are obtained analyticallyusing Rogers dilogarithm identities. We incorporate all finite excitations byformulating empirical selection rules for the patterns of zeros of all theeigenvalues of the standard modules. We thus obtain the conformal partitionfunctions on the cylinder and the modular invariant partition function (MIPF)on the torus. By applying $q$-binomial identities, it is shown that ourfinitized characters on the strip agree with those of Pearce, Rasmussen andZuber. On the torus, the MIPF is a non-diagonal sesquilinear form in affine$u(1)$ characters given by the $u(1)$ partition function$Z_{2,3}(q)=Z_{2,3}^{\rm{Circ}}(q)$. This is compatible with the generalconjecture of Pearce and Rasmussen, namely$Z_{p,p'}(q)=Z^{\rm{Proj}}_{p,p'}(q)+n_{p,p'}Z^{\rm{Min}}_{p,p'}(q)$ with$n_{p,p'}\in {\Bbb Z}$, and the lattice derivation fixes $n_{2,3}=-1$.

Conformal partition functions of critical percolation from $D_3$ Thermodynamic Bethe Ansatz equations