  Motivated in part by quantum criticality in dissipative Kondo systems, we
revisit the finite-size scaling of a classical Ising chain with 1/r^{2-epsilon}
interactions. For 1/2<epsilon<1, the scaling of the dynamical spin
susceptibility is sensitive to the degree of "winding" of the interaction under
periodic boundary conditions. Infinite winding yields the expected mean-field
behavior, whereas without any winding the scaling is of an interacting omega/T
form. The contrast with the behavior of the Bose-Fermi Kondo model suggests a
breakdown of a mapping from the quantum model to a classical one due to the
smearing of the Kondo spin flips by the continuum limit taken in this mapping.

Strongly Correlated Electrons;Statistical Mechanics