Absence of long-range order in three-dimensional Heisenberg models.

Abstract

The famous theorem of Mermin and Wagner excludes long-range order (LRO) in one- and two-dimensional Heisenberg models at any finite temperature if the exchange interaction is short ranged. Strong but nonrigorous indications exist about the absence of LRO even in three-dimensional Heisenberg models when suitable competing exchange interactions are present. We find, as a rigorous consequence of the Bogoliubov inequality, that this expectation is true. We find that for models where the exchange competition concerns at least two over three dimensions, a surface of the parameter space exists where LRO is absent. This surface meets at vanishing temperature the continuous phase-transition line which is the border line between the ferromagnetic and helical configuration.