Quantum-Field-Theory Approach to the Heisenberg Ferromagnet

Abstract

Earlier derivations of simple Wick's theorems for operators of spin J and 1 (in units of fi) using the drone-fermion representation are applied to the Heisenberg model. The resulting diagrammatic-perturbational approach (Green's functions) is carried out in both the high-and low-temperature domains, where the expansion criteria of Stinchcombe et al. are closely followed. The present work effectively reexpresses the semi-invariant analysis of these authors in a much simpler manner, and many of their results are straightforwardly reproduced. The use of standard quantum-field-theory techniques enables renormalization to be undertaken in a simple, systematic manner. At low temperatures the present fermion analysis gives Dyson's T 4 contribution to the free energy from the first Born approximation to spin-wave scattering. Higher-order spin-wave contributions give a damping term, which, upon evaluation in the lowest approximation, is identical to that found by ter Haar and Tahir-Kheli. 9

Charge fluctuation between even and odd states of a superconducting island

“…II. The first order term of the grand canonical potential Ω (1) becomes the similar form as W (1) and consists of the thermal GF for c-field, dfield and the particle-hole given by 1/(iω l −∆ 0 ), 2/(iω l ) 14 and α(iν n ), respectively. Here, ω l and ν n are the fermion and the boson Matsubara frequency, respectively.…”

“…The Hamiltonian includes the effective spin-1/2 operator σ and thus the Wick's theorem for fermions or bosons cannot be used. To circumvent this drawback, we employ the drone-fermion representation 13,14 , which is the map of σ onto two fermion operators c and d as σ + = c † φ and σ z = 2c † c − 1, where φ = d † + d is a Majorana fermion operator. In our calculation, we reformulate Ref.…”

Efficiency of excitation of the laser-active levels of the copper atom in electric discharges

“…In calculations of the low temperature damping for the Heisenberg ferromagnet (Spencer 1968, Vaks et al 1968) it was necessary to go to order ( l /~)~ to get the leading order contribution. This difference arises because of energy denominators of the form (iy f eq f E q -k ) and (iy f cq 7)) which occur in our results for the selfenergy matrix elements C,,(k, y) in the Appendix.…”

“…At low temperature T < T, the results for the damping differ fundamentally from the corresponding results in the absence of dipole-dipole coupling (ie for the Heisenberg ferromagnet). The contributions arise from three-magnon processes and are of order ( l /~)~, whereas for the Heisenberg model the leading order damping is of order ( l /~)~ and involves four-magnon processes (Spencer 1968, Vaks et al 1968). …”

Low-temperature critical phenomena in the spin-1/2 planar ferromagnet

“…The F,-j that appear in (11) (17) E=ff dt(5~a+~-~b) (18) (20) The complex field r (it is periodic in t with period B) was introduced in a manner analogous to the real field o'i. It was used to express the XY contribution to e -s in (6) as a Gaussian functional integral.…”