Apparent phase transition in a chain of magnetic dipoles?

Abstract Considering chains of classical spins coupled by long-range interactions ∼ r − σ , we show a qualitative difference between the critical behaviour of systems with isotropic and anisotropic interactions, as seen from the analysis of the Binder cumulant by Monte Carlo simulations. Unlike the known absence of long range order in isotropic case for σ >2, we found indications of finite critical temperatures in the anisotropic case even for σ as high as 3, related to dipolar coupling.