Percolation and the existence of a soft phase in the classical Heisenberg model

Details Percolation and the existence of a soft phase in the classical Heisenberg model Percolation and the existence of a soft phase in the classical Heisenberg model

2000-11-22

arxiv.org/abs/hep-th/0011199v1

J.Statist.Phys. 106 (2002) 811-826

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 7 figures

Scientific paper

We present the results of a numerical investigation of percolation properties in a version of the classical Heisenberg model. In particular we study the percolation properties of the subsets of the lattice corresponding to equatorial strips of the target manifold ${\cal S}^2$. As shown by us several years ago, this is relevant for the existence of a massless phase of the model. Our investigation yields strong evidence that such a massless phase does indeed exist. It is further shown that this result implies lack of asymptotic freedom in the massive continuum limit. A heuristic estimate of the transition temperature is given which is consistent with the numerical data.

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