The two-dimensional bond-diluted quantum Heisenberg model at the classical percolation threshold

TL;DR

This study uses quantum Monte Carlo simulations to demonstrate that the two-dimensional bond-diluted quantum Heisenberg model maintains long-range antiferromagnetic order at the classical percolation threshold, confirming classical critical exponents.

Contribution

It provides evidence that the order-disorder transition in the 2D bond-diluted quantum Heisenberg model occurs precisely at the percolation threshold with classical exponents, extending understanding of quantum criticality in disordered systems.

Findings

Long-range order exists at the percolation threshold.

Transition occurs exactly at the percolation threshold.

Critical exponents are classical.

Abstract

The two-dimensional antiferromagnetic S=1/2 Heisenberg model with random bond dilution is studied using quantum Monte Carlo simulation at the percolation threshold (50% of the bonds removed). Finite-size scaling of the staggered structure factor averaged over the largest connected clusters of sites on L*L lattices shows that long-range order exists within the percolating fractal clusters in the thermodynamic limit. This implies that the order-disorder transition driven by bond-dilution occurs exactly at the percolation threshold and that the exponents are classical. This result should apply also to the site-diluted system.