Absence of a Magnetic Phase Transition in Heisenberg, Hubbard, and Kondo-lattice (s-f) Films

TL;DR

This paper demonstrates that Heisenberg, Hubbard, and Kondo-lattice films do not exhibit magnetic phase transitions at finite temperatures for any finite number of layers, extending the Mermin-Wagner theorem to these systems.

Contribution

It extends the Mermin-Wagner theorem to a broader class of layered magnetic systems, showing the absence of magnetic order at finite temperature for any finite number of layers.

Findings

Magnetization vanishes in all layers at finite temperature

No magnetic phase transition occurs in these films at finite temperature

The theorem applies to Heisenberg, Hubbard, and Kondo-lattice models

Abstract

The possibility of a magnetic phase transition in Heisenberg, Hubbard, and s-f (Kondo-lattice) films is investigated. It is shown that, for any finite temperature and any finite number of layers, the magnetization within every layer must vanish. Thus, the Mermin-Wagner theorem is extended to a variety of system geometries. We also comment on the microscopic interpretation of the transition from two to three dimensions in the limit of an infinite number of layers.