Scale-independent fluctuations of spin stiffness in the Heisenberg model and its relationship to universal conductance fluctuations

It is shown that, at low temperatures, the absolute thermal fluctuations of the spin-stiffness constant in the classical Heisenberg model are independent of the scale L for d<4, if L is larger than the lattice spacing but smaller than the correlation length, while the relative fluctuation is proportional to ${\mathit{L}}^{4\mathrm{-}2\mathit{d}}$, where d is the dimensionality, and is thus scale independent in d=2 (with logarithmic corrections). The phenomenon is strikingly similar to the universal conductance fluctuations known for the problem of an electron in a random potential.