Bounds on ferromagnetism atT>0 in the hard-core electron lattice gas

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Abstract
In a recent paper by Aizenman and Lieb [Phys. Rev. Lett. 65, 1470 (1990)], it was reported that the Nagaoka ferromagnet preserves its ferromagnetic character at temperatures T>0 in any finite volume. It is shown here that at any T>0 the Nagaoka ferromagnet becomes a perfect paramagnet in the thermodynamic limit. By using an inequality for the free energy, this result is extended to the general case when the number of electrons per site goes to 1. At any T>0 the spontaneous magnetization m(T,ρ) tends to zero as the electron density ρ tends to 1. Thus, a rigorous upper bound on m(T,ρ) is obtained. The results are independent of the statistics.