High-temperature series expansion for the spin-1/2 Heisenberg model of the simple cubic lattice

Abstract

The Heisenberg model, described by the Hamiltonian
H = − 2J ∑_〈ij〉s_i⋅s_j − 2μh ∑_i s_i^z 
is used to calculate the partition function Z = Tr e^−βH from which the thermodynamic functions are obtained as expansions in the variable K = βJ = J/kT. Here, s_i is a spin operator at the site i of the simple cubic crystal lattice, J the exchange energy between neighboring spins (and positive for ferromagnetic coupling), μ the magnetic moment, and s_i^z the component of s_i, in the direction of the external magnetic field h. Formally, from the expression
N^-1 ln Z = F₀(K) + (βμh)²F₂(K)/2 + ⋯,
the zero-field specific heat
C = Nk K² ∂²F₀(K)/∂ K² 
and the susceptibility
χ = Nμ²F₂(K)/kT
are found, N being the number of lattice sites. The problem is reduced to calculating the functions F₀(K) and F₂(K) as power series in K using the finite-lattice method.