Absence of Spontaneous Magnetic Order at Nonzero Temperature in One- and Two-Dimensional Heisenberg andXYSystems with Long-Range Interactions

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Abstract
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−α with a sufficiently large exponent α. For oscillatory interactions, ferromagnetic long-range order at T>0 is ruled out if α≥1(D=1) or α>5/2(D=2). For systems with monotonically decreasing interactions, ferro- or antiferromagnetic long-range order at T>0 is ruled out if α≥2D.