Critical properties of a dilute O($n$) model on the kagome lattice

Abstract

A critical dilute O($n$) model on the kagome lattice is investigated analytically and numerically. We employ a number of exact equivalences which, in a few steps, link the critical O($n$) spin model on the kagome lattice to the exactly solvable critical $q$-state Potts model on the honeycomb lattice with $q=(n+1{)}^2$. The intermediate steps involve the random-cluster model on the honeycomb lattice, and a fully packed loop model with loop weight $n^{\prime }=\sqrt{q}$ and a dilute loop model with loop weight $n$, both on the kagome lattice. This mapping enables the determination of a branch of critical points of the dilute O($n$) model, as well as some of its critical properties. For $n=0$, this model reproduces the known universal properties of the $\theta$ point describing the collapse of a polymer. For $n\ne 0$ it displays a line of multicritical points, with the same universal properties as a branch of critical behavior that was found earlier in a dilute O($n$) model on the square lattice. These findings are supported by a finite-size-scaling analysis in combination with transfer-matrix calculations.

arXiv comment19 pages, 6 figures

References in corpus (3)

• Collapse of a polymer in two dimensions
• Exact characterization of O(n) tricriticality in two dimensions
• First and second order transitions in dilute O(n) models

Cited by in corpus (2)

• Critical frontier for the Potts and percolation models on triangular-type and kagome-type lattices II: Numerical analysis
• Exact critical points of the O($n$) loop model on the martini and the 3-12 lattices