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The Mermin-Wagner theorem is strengthened so as to rule out magneticlong-range order at T>0 in one- or two-dimensional Heisenberg and XY systemswith long-range interactions decreasing as R^{-alpha} with a sufficiently largeexponent alpha. For oscillatory interactions, ferromagnetic long-range order atT>0 is ruled out if alpha >= 1 (D=1) or alpha > 5/2 (D=2). For systems withmonotonically decreasing interactions ferro- or antiferromagnetic long-rangeorder at T>0 is ruled out if alpha >= 2D.

physical review letters

Absence of Spontaneous Magnetic Order at Nonzero Temperature in One- and Two-Dimensional Heisenberg and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">XY</mml:mi></mml:math>Systems with Long-Range Interactions

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