Percolation properties of the 2D Heisenberg model

Abstract

We analyze the percolation properties of certain clusters defined on configurations of the 2--dimensional Heisenberg model. We find that, given any direction \vec{n} in O(3) space, the spins almost perpendicular to \vec{n} form a percolating cluster. This result gives indications of how the model can avoid a previously conjectured Kosterlitz-Thouless phase transition at finite temperature T.

4 pages, 3 eps figures. Revised version (more clear abstract, some new references)

References in corpus (5)

• Asymptotic Scaling in the Two-Dimensional $O(3)$ $\sigma$-Model at Correlation Length $10^5$
• Perturbation theory predictions and Monte Carlo simulations for the 2-d O(n) non-linear sigma-model
• Classical XY Model in 1.99 Dimensions
• Testing fixed points in the 2D O(3) non-linear sigma model
• Finite-size scaling of the helicity modulus of the two-dimensional O(3) model

Cited by in corpus (4)

• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• Comment on "Percolation Properties of the 2D Heisenberg Model"
• Reply to A. Patrascioiu's and E. Seiler's Comment on our paper "Percolation properties of the 2D Heisenberg model"
• Nontrivial fixed point in nonabelian models