, Volume 100, Issue 3, pp 447-462

Long range order in the anisotropic quantum ferromagnetic Heisenberg model

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Abstract

We study the anisotropic quantum mechanical ferromagnetic Heisenberg model. By anisotropic we mean that thex andy exchange constants are equal but smaller than thez exchange constant. We show that for any amount of anisotropy there is long range order in two or more dimensions at low enough temperature. We also develop a convergent low temperature expansion and use it to prove exponential decay of the truncated correlation functions.

Research partially supported by U.S. National Science Foundation under Grant PHY8116101 AO 3
Communicated by J. Fröhlich