which reduce the effective statistics and thus increase the statistical errors considerably [@r2]. The recent development [@r1] of [*global*]{} update algorithms that overcome the problem of critical slowing down is a major step forward. It is this algorithmic improvement combined with the higher speed of modern computers that makes systematic tests of finite-size scaling (FSS) predictions [@barber] and a reliable computation of critical exponents much more feasible than a few years ago.

For spin systems cluster algorithms [@r3; @r4] turned out to be particularly successful. Recent applications of the multiple [@r3] and single [@r4] cluster variants to two-dimensional (2D) Ising [@r5; @tamayo; @r6], XY [@r8; @r7; @r9; @r9a], Heisenberg [@r10; @r10a] and other $O(n)$ [@r11] models have demonstrated that both variants are equally good tools to simulate these 2D systems. In three dimensions (3D), however, extensive tests for the Ising [@r5; @tamayo; @r12] and XY [@r13; @r14] models clearly showed that the single-cluster variant is the superior algorithm. In our study of the 3D Heisenberg model we have therefore chosen the single-cluster update algorithm [@ours]. The set-up of our simulations is described in some detail in Sec. 2.

There are of course many sources for a comparison with simulations based 