Affiliations: Université de Toulon et du Var, and Centre de Physique Théorique-CNRS, Campus de Luminy, Case 907 13288, Marseille cedex 9, France. E-mail: briet@univ-tln.fr | Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg, Denmark. E-mail: cornean@math.aau.dk | Centre de Physique Théorique-CNRS, Campus de Luminy, Case 907 13288, Marseille cedex 9, France. E-mail: louis@cpt.univ-mrs.fr
Note: [] Corresponding author.
Abstract: Consider a charged, perfect quantum gas, in the effective mass approximation, and in the grand-canonical ensemble. We prove in this paper that the generalized magnetic susceptibilities admit the thermodynamic limit for all admissible fugacities, uniformly on compacts included in the analyticity domain of the grand-canonical pressure. The problem and the proof strategy were outlined in MPRF 11 (2005), 177–188. In J. Math. Phys. 47 (2006), 083511 we proved in detail the pointwise thermodynamic limit near z=0. The present paper is the last one of this series, and contains the proof of the uniform bounds on compacts needed in order to apply Vitali's Convergence Theorem.
Keywords: thermodynamic limit, magnetic field, susceptibilities
