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

We obtain an asymptotic formula, as $n\to\infty$, for the monomer-monomercorrelation function $K_2(x,y)$ in the classical dimer model on a triangularlattice, with the horizontal and vertical weights $w_h=w_v=1$ and the diagonalweight $w_d=t>0$, where $x$ and $y$ are sites $n$ spaces apart in adjacentrows.  We find that $t_c=\frac{1}{2}$ is a critical value of $t$. We prove that inthe subcritical case, $0<t<\frac{1}{2}$, as $n\to\infty$,$K_2(x,y)=K_2(\infty)\left[1-\frac{e^{-n/\xi}}{n}\,\Big(C_1+C_2(-1)^n+\mathcalO(n^{-1})\Big)\right]$, with explicit formulae for $K_2(\infty)$, $\xi$, $C_1$,and $C_2$. In the supercritical case, $\frac{1}{2} < t < 1$, we prove that as$n\to\infty$, $K_2(x,y)=K_2(\infty)\Bigg[1- \frac{e^{-n/\xi}}{n}\,\Big(C_1\cos(\omega n+\varphi_1)+C_2(-1)^n\cos(\omega n+\varphi_2)+C_3+C_4(-1)^n$ $+\mathcal O(n^{-1})\Big)\Bigg]$, with explicit formulae for$K_2(\infty)$, $\xi$, $\omega$, and $C_1$, $C_2$, $C_3$, $C_4$, $\varphi_1$,$\varphi_2$. The proof is based on an extension of theBorodin-Okounkov-Case-Geronimo formula to block Toeplitz determinants and on anasymptotic analysis of the Fredholm determinants in hand.

Exact solution of the classical dimer model on a triangular lattice: Monomer-monomer correlations