The present paper reports Monte Carlo calculations for a classical system, consisting of three-component unit vectors, associated with a two-dimensional lattice {${\mathit{u}}_{\mathit{k}}$k∈${\mathit{Z}}^2$}, and interacting via a translationally invariant pair potential of the long-range, ferromagnetic and isotropic form ${\mathit{W}}_{\mathit{j}\mathit{k}}$=-ε‖${\mathbf{x}}_{\mathit{j}}$${\mathbf{x}}_{\mathit{k}}$${\mathrm{\Vert }}^{\mathrm{-}4}$${\mathbf{u}}_{\mathit{j}}$⋅${\mathbf{u}}_{\mathit{k}}$. Here ε is a positive quantity setting energy and temperature scales (i.e., ${\mathit{T}}^{\mathrm{*}}$=${\mathit{k}}_{\mathit{B}}$T/ε), and ${\mathbf{x}}_{\mathit{k}}$ denotes the dimensionless lattice-site coordinates. The system is known rigorously to become disordered at all finite temperatures; moreover, an approximate harmonic argument suggests the existence of a transition to a low-temperature phase possessing a slow decay of correlations and infinite susceptibility. Simulation results were found to be consistent with this conjecture, and to suggest that ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$=1.440±0.005.

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