Green's-function theory of the Heisenberg ferromagnet in a magnetic field

TL;DR

This paper develops a second-order Green's-function theory for one- and two-dimensional S=1/2 ferromagnets in magnetic fields, accurately predicting thermodynamic properties and spin correlations, validated by exact and numerical methods.

Contribution

It introduces a decoupling scheme with vertex parameters for improved modeling of ferromagnetic systems, aligning well with exact solutions and quantum Monte Carlo data.

Findings

Good agreement with exact diagonalizations and Bethe-ansatz results

Power-law behavior in susceptibility and specific heat maxima

Enhanced description of short-range magnetic order

Abstract

We present a second-order Green's-function theory of the one- and two-dimensional S=1/2 ferromagnet in a magnetic field based on a decoupling of three-spin operator products, where vertex parameters are introduced and determined by exact relations. The transverse and longitudinal spin correlation functions and thermodynamic properties (magnetization, isothermal magnetic susceptibility, specific heat) are calculated self-consistently at arbitrary temperatures and fields. In addition, exact diagonalizations on finite lattices and, in the one-dimensional case, exact calculations by the Bethe-ansatz method for the quantum transfer matrix are performed. A good agreement of the Green's-function theory with the exact data, with recent quantum Monte Carlo results, and with the spin polarization of a $\nu=1$ quantum Hall ferromagnet is obtained. The field dependences of the position and height of the maximum in the temperature dependence of the susceptibility are found to fit well to power laws, which are critically analyzed in relation to the recently discussed behavior in Landau's theory. As revealed by the spin correlation functions and the specific heat at low fields, our theory provides an improved description of magnetic short-range order as compared with the random phase approximation. In one dimension and at very low fields, two maxima in the temperature dependence of the specific heat are found. The Bethe-ansatz data for the field dependences of the position and height of the low-temperature maximum are described by power laws. At higher fields in one and two dimensions, the temperature of the specific heat maximum linearly increases with the field.