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

Authors

Jaan Oitmaa ⋅ AU Department of Theoretical Physics, University of New South Wales
Ermys Bornilla ⋅ PH Physics Department, De La Salle University, Manila

Abstract

The Heisenberg model, described by the Hamiltonian
H = − 2J ∑_〈ij〉s_i⋅s_j − 2μh ∑_is_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.

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Issue

1994: Proceedings of the 12th National Physics Congress of the Samahang Pisika ng Pilipinas

Article ID

SPP-1994-TP-02

Section

Theoretical Physics

Published

1994-10-15

How to Cite

[1]

J Oitmaa and E Bornilla, High-temperature series expansion for the spin-1/2 Heisenberg model of the simple cubic lattice, Proceedings of the Samahang Pisika ng Pilipinas 12, SPP-1994-TP-02 (1994). URL: https://proceedings.spp-online.org/article/view/SPP-1994-TP-02.