Absence of spontaneous ferromagnetic order at non-zero temperature in one- and two-dimensional Heisenberg and XY systems with long range interactions

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Abstract
The Mermin-Wagner theorem is strengthened so as to rule out ferromagnetic long range order at T>0 in 1D or 2D Heisenberg and XY systems with long range interactions decreasing as R^{-alpha} with a sufficiently large exponent alpha. For oscillatory interactions, ferromagnetic long range order at T>0 is ruled out if alpha>1 (1D) or alpha >= 5/2 (2D). For 1D systems with monotonically decreasing interactions ferromagnetic long range order is ruled out at T>0 if alpha >= 2.

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