SUSCEPTIBILITY AND FLUCTUATION

Bounds are presented relating zero-field static isothermal magnetic susceptibilities to the mean-square fluctuations of corresponding magnetization variables. The lower bounds contain the first frequency moment of a spectral density. When this moment ω̄ approaches zero, the upper and lower bounds merge, and the susceptibility is determined by the mean-square fluctuation. In particular, if the susceptibility diverges at a temperature Tc, and if the expectation of the double commutator appearing in ω̄ is finite at and near Tc, then the fluctuation and the susceptibility diverge in the same manner, and their critical exponents will be identical. © 1969 The American Physical Society.