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

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

2001-05-06

arxiv.org/abs/cond-mat/0105129v3

Phys. Rev. Lett. 87, 137203 (2001)

Physics

Condensed Matter

Statistical Mechanics

RevTeX, 4 pages. Further (p)reprints available from http://www.mpi-halle.de/~theory ; v2: revised version

Scientific paper

10.1103/PhysRevLett.87.137203

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 (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 >= 2D.

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