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

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).

Two-time Green’s functions and spectral density method in nonextensive quantum statistical mechanics

“…A preliminary study along this direction can be found in Ref. [46] where we have applied the q SDM to an isotropic Heisenberg model with long-range exchange interactions.…”

“…It is worth noting that, although the condition ( 56) is certainly verified in the limit q → 1, it can be also realized for q far from unity with suitable choices of the parameters β and E n − U q . However, in view of a still reduced number of applications [27,46], in order to gain experience in using the q many body formalism developed before for more complex situations, it may be in any case useful to consider weak nonextensivity conditions with q close to unity.…”

“…A preliminary study, along this direction, of a d-dimensional Heisenberg spin model with long-range interactions was performed in Ref. [46]. These are only two nontrivial many-body problems used by us to test the effectiveness of our suggestion to perform direct nonextensivity calculations within a genuine q many-body theory.…”