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

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 $d⟨n⟩\mathrm{/}dT$ 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 $d⟨n⟩\mathrm{/}dT$ at $K_c$ from simulations on lattices of size up to ${16}^3$. We obtain weak evidence that $d⟨n⟩\mathrm{/}dT$ 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 $\alpha \mathrm{/}\nu$ of the specific-heat exponent with the correlation-length exponent from a finite-size scaling analysis of the energy.