J.-B. Bru and W. de Siqueira Pedra
Fermi Systems With Long Range Interactions
(970K, pdf)
ABSTRACT. We define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, we give a first
answer to an old open problem in mathematical physics -- first addressed by Ginibre in 1968 within a different context -- about
the validity of the so--called Bogoliubov approximation on the level of
states. Depending on the model $\mathfrak{m}\in \mathcal{M}_{1}$, our method provides a systematic way to study all its correlation functions and can thus be used to analyze the physics of long range interactions.
Furthermore, we show that the thermodynamics of long range
models $\mathfrak{m}\in \mathcal{M}_{1}$ is governed by the non--cooperative equilibria of a zero--sum game, called here thermodynamic game.