Abstract
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 \(S\) 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 exits. 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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Patrascioiu, A., Seiler, E. Percolation and the Existence of a Soft Phase in the Classical Heisenberg Model. Journal of Statistical Physics 106, 811–826 (2002). https://doi.org/10.1023/A:1013726826390
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DOI: https://doi.org/10.1023/A:1013726826390