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arXiv · hep-lat/9306020

Monte Carlo Study of Topological Defects in the 3D Heisenberg Model

Christian Holm·Wolfhard Janke
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Abstract

We use single-cluster Monte Carlo simulations to study the role of topological defects in the three-dimensional classical Heisenberg model on simple cubic lattices of size up to $80^3$. By applying reweighting techniques to time series generated in the vicinity of the approximate infinite volume transition point $K_c$, we obtain clear evidence that the temperature derivative of the average defect density $d\langle n \rangle/dT$ behaves qualitatively like the specific heat, i.e., both observables are finite in the infinite volume limit. This is in contrast to results by Lau and Dasgupta [{\em Phys. Rev.\/} {\bf B39} (1989) 7212] who extrapolated a divergent behavior of $d\langle n \rangle/dT$ at $K_c$ from simulations on lattices of size up to $16^3$. We obtain weak evidence that $d\langle n \rangle/dT$ scales with the same critical exponent as the specific heat.As a byproduct of our simulations, we obtain a very accurate estimate for the ratio $α/ν$ of the specific-heat exponent with the correlation-length exponent from a finite-size scaling analysis of the energy.

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Christian Holm, Wolfhard Janke. 1993-06-24. Monte Carlo Study of Topological Defects in the 3D Heisenberg Model. https://doi.org/10.1088/0305-4470%2F27%2F7%2F030

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