Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions

TL;DR

This paper investigates the magnetic phase transitions and critical properties of quantum Heisenberg ferromagnets with long-range interactions decaying as 1/r^p in one and two dimensions, using Green's function and spin-wave methods.

Contribution

It provides a detailed analysis of phase transition conditions, critical temperature estimates, and critical exponents dependence on p, with results validated by two different theoretical approaches.

Findings

Finite-temperature phase transition exists for d<p<2d

No finite-temperature transition for p≥2d

Critical exponents depend on p and satisfy scaling relations

Abstract

Quantum Heisenberg ferromagnets with long-range interactions decayin as $1/r^p$ in one and two dimensions are investigated by means of the Green's function method. It is shown that there exists a finite-temperature phase transition in the region $d<p<2 d$ for the $d$-dimensional case and that no transitions at any finite temperature exist for $p\ge 2 d$; the critical temperature is also estimated. We study the magnetic properties of this model. We calculate the critical exponents' dependence on $p$; these exponents also satisfy a scaling relation. Some of the results were also found using the modified spin-wave theory and are in remarkable agreement with each other.