Eur. Phys. J. B 50, 73-76 (2006)
https://doi.org/10.1140/epjb/e2006-00132-y

Spectral density method in quantum nonextensive thermostatistics and magnetic systems with long-range interactions

Dipartimento di Fisica “E.R. Caianiello", Universita' degli Studi di Salerno, and INFM, Unita' di Salerno, via S. Allende, 84081 Baronissi (SA), Italy

Corresponding author: ^a cosfab@sa.infn.it

Received: 30 September 2005
Revised: 7 December 2005
Published online: 12 April 2006

Abstract

Motived by the necessity of explicit and reliable calculations, as a valid contribution to clarify the effectiveness and, possibly, the limits of the Tsallis thermostatistics, we formulate the Two-Time Green Functions Method in nonextensive quantum statistical mechanics within the optimal Lagrange multiplier framework, focusing on the basic ingredients of the related Spectral Density Method (SDM). Besides, to show how the SDM works, we have performed, to the lowest order of approximation, explicit calculations of the low-temperature properties for a quantum d-dimensional spin-1/2 Heisenberg ferromagnet with long-range interactions decaying as 1/r^p ( r is the distance between spins in the lattice).