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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
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 >= 1 …