Thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets in an external magnetic field within Green function formalism

TL;DR

This paper develops a Green function approach to study the thermodynamics of low-dimensional spin-1/2 Heisenberg ferromagnets in magnetic fields, accurately describing various thermodynamic properties across different lattice geometries.

Contribution

It introduces a second-order Green function formalism that properly accounts for analytical properties, providing accurate thermodynamic predictions for finite and infinite systems.

Findings

Good agreement with Bethe ansatz, exact diagonalization, and Monte Carlo data.

Accurate description of correlation functions, magnetization, susceptibility, and heat capacity.

Study of cluster size effects in 2D systems.

Abstract

The thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets (HFM) in an external magnetic field is investigated within a second-order two-time Green function formalism in the wide temperature and field range. A crucial point of the proposed scheme is a proper account of the analytical properties for the approximate transverse commutator Green function obtained as a result of the decoupling procedure. A good quantitative description of the correlation functions, magnetization, susceptibility, and heat capacity of the HFM on a chain, square and triangular lattices is found for both infinite and finite-sized systems. The dependences of the thermodynamic functions of 2D HFM on the cluster size are studied. The obtained results agree well with the corresponding data found by Bethe ansatz, exact diagonalization, high temperature series expansions, and quantum Monte Carlo simulations.