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

TL;DR

This paper develops a spectral density method within nonextensive quantum thermostatistics to analyze magnetic systems with long-range interactions, providing explicit low-temperature calculations for a spin-1/2 Heisenberg ferromagnet.

Contribution

It formulates the Two-Time Green Functions Method in nonextensive quantum mechanics and applies it to long-range interacting magnetic systems, demonstrating its effectiveness and limitations.

Findings

Explicit low-temperature properties calculated for long-range Heisenberg ferromagnet

Demonstrates the applicability of spectral density method in nonextensive quantum systems

Provides insights into the effects of long-range interactions on magnetic properties

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. 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)