Definition and statistical distributions of a topological number in the lattice O(3) σ-model |
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Authors: | B Berg M Lüscher |
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Institution: | CERN, Geneva, Switzerland;Institut für theoretische Physik, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland |
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Abstract: | We define a topological number Q for spin fields on a two-dimensional lattice. Q assumes integer values only and reduces to the well-known winding number in the classical continuum limit. A Monte Carlo measurement of the topological susceptibility χt = 〈Q2〉 / volume on a 100 × 100 lattice reveals that it decreases exponentially with increasing β( = inverse bare coupling constant). The corresponding prediction of the perturbative renormalization group is not matched, however. |
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