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.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.

arXiv:cond-mat/9909230Sep 15, 19990 citations

Percolation Properties of the 2D Heisenberg Model

B. Allés, Juan J. Alonso, Carlos Criado +1 more

We analyze the percolation properties of certain clusters defined on configurations of the two-dimensional Heisenberg model. We find that, given any direction in $\stackrel{\ensuremath{\rightarrow}}{n}$ in $O(3)$ space, spins that are almost perpendicular to $\stackrel{\ensuremath{\rightarrow}}{n}$ form a percolating cluster. This result indicates how the model can avoid a previously conjectured Kosterlitz-Thouless phase transition at a finite temperature $T$ .We analyze the percolation properties of certain clusters defined on configurations of the two-dimensional Heisenberg model. We find that, given any direction in $\stackrel{\ensuremath{\rightarrow}}{n}$ in $O(3)$ space, spins that are almost perpendicular to $\stackrel{\ensuremath{\rightarrow}}{n}$ form a percolating cluster. This result indicates how the model can avoid a previously conjectured Kosterlitz-Thouless phase transition at a finite temperature $T$.

arXiv:hep-lat/9905026Physical Review LettersNov 1, 199911 citations

Percolation Theory of Phase Transitions in Spin Models

Chin‐Kun Hu

Chinese Journal of PhysicsAug 1, 19841 citation

Disordered phase of a two-dimensional Heisenberg model with

S. Moukouri

arXiv:cond-mat/0510288Physics Letters ANov 30, 200514 citations

O(3)

space, spins that are almost perpendicular to $\stackrel{\ensuremath{\rightarrow}}{n}$ form a percolating cluster. This result indicates how the model can avoid a previously conjectured Kosterlitz-Thouless phase transition at a finite temperature

T