Absence of spontaneous magnetic order at nonzero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactions.

The Mermin-Wagner theorem is strengthened so as to rule out magnetic long-range order at T > 0 in one- or two-dimensional 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 > or = 1(D = 1) or alpha > 5/2(D = 2). For systems with monotonically decreasing interactions, ferro- or antiferromagnetic long-range order at T > 0 is ruled out if alpha > or = 2D.