Critical properties of the Hintermann-Merlini model

TL;DR

This paper numerically investigates the critical properties of the Hintermann-Merlini model, confirming existing analytic predictions and revealing new geometric properties such as fractal dimensions of Ising clusters.

Contribution

It provides a comprehensive numerical analysis of the model's critical behavior, confirming predictions and exploring unstudied geometric properties.

Findings

Central charge c=1 for the critical manifold

Fractal dimension of largest Ising cluster on sublattice A is approximately 1.888

Fractal dimension on sublattice B varies continuously with parameters

Abstract

Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to the eight-vertex model. Wu [J. Phys. C {\bf 8}, 2262 (1975)] calculated the spontaneous magnetizations of the model on two sublattices by relating them to the conjectured spontaneous magnetization and polarization of the eight-vertex model, respectively. The latter conjecture remains unproved. In this paper, we numerically study the critical properties of the model by means of a finite-size scaling analysis based on transfer matrix calculations and Monte Carlo simulations. All analytic predictions for the model are confirmed by our numerical results. The central charge $c=1$ is found for the critical manifold investigated. In addition, some unpredicted geometry properties of the model are studied. Fractal dimensions of the largest Ising clusters on two sublattices are determined. The fractal dimension of the largest Ising cluster on the sublattice A takes fixed value $D_{\rm a}=1.888(2)$, while that for sublattice B varies continuously with the parameters of the model.