Existence of Long-Range Order in Quasi-Two-Dimensional Hubbard Model

Details Existence of Long-Range Order in Quasi-Two-Dimensional Hubbard Model Existence of Long-Range Order in Quasi-Two-Dimensional Hubbard Model

1994-09-19

arxiv.org/abs/cond-mat/9409076v1

Physics

Condensed Matter

6 pages,CPT-94/P.3025,LaTex

Scientific paper

In recent work of Monthoux and Pines~[1] and also in Rice et {\sl al.}'s work~[2], quasi-averages like $\langle c_{k \uparrow} c_{- k \downarrow} \rangle$ were considered even in the case of a dimension less or equal two. But it is well known from the old work of Hohenberg~[3] that these quasi-averages are zero at $T \not= 0$ in case of 1 and 2 dimensions. In this communication we apply the result of Hohenberg to the Hubbard model and prove that in the case of quasi-two-dimension, the inequality of Bogoliubov is not in contradiction with having $\langle c_{k \uparrow} c_{- k \downarrow} \rangle \not= 0$ (at $T \not= 0$) even for a system of three layers.

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