Moments of general Heisenberg Hamiltonians up to sixth order

TL;DR

This paper computes the moments of general Heisenberg Hamiltonians up to sixth order, expressing them as sums involving multigraphs and polynomials, and applies these results to expand free energy and susceptibility in inverse temperature.

Contribution

It provides explicit formulas for moments of Heisenberg Hamiltonians up to sixth order, linking graph theory with quantum spin models.

Findings

Explicit sixth-order moments expressed as multigraph sums.

Derived coefficients for free energy and susceptibility expansions.

Results highlight the extensive nature of thermodynamic coefficients.

Abstract

We explicitly calculate the moments t_n of general Heisenberg Hamiltonians up to sixth order. They have the form of finite sums of products of two factors, the first factor being represented by a multigraph and the second factor being a polynomial in the variable s(s + 1), where s denotes the individual spin quantum number. As an application we determine the corresponding coefficients of the expansion of the free energy and the zero field susceptibility in powers of the inverse temperature. These coefficients can be written in a form which makes explicit their extensive character.