EXACT SOLUTION FOR THE INELASTIC NEUTRON-SCATTERING FROM AN ANISOTROPIC HONEYCOMB ISING MAGNET

We consider an anisotropic Ising model ferromagnet on the honeycomb lattice, having nearest-neighbour pairwise interactions J, theta-J > 0 along the oblique and horizontal lattice axes, respectively, with theta > 0 being an anisotropy parameter. Since the Hamiltonian contains solely z-component (longitudinal) Pauli spin operators, the dynamics in the Ising model evolves only for the non-ordering (transverse) spin degrees of freedom. An exact solution is calculated for the inelastic neutron scattering function S(xx)(q, omega) = SIGMA-n A(n)(T, theta) delta (omega - omega-n(theta)), n = +/- 3, +/- 2, +/- 1, which depends upon the frequency omega, temperature T and anisotropy-theta. The discrete energy transfers h-omega-n(theta) are independent of temperature, vary linearly with theta and possess degeneracies for certain integral values of theta. The scattering amplitudes (intensities/site) A(n)(T, theta) of the Dirac delta-functions exhibit, for fixed theta, such behaviours as rounded maxima, crossing points, and weak energy-type singularities at the critical temperature T(c)(theta). At critically, the 'spin wave mode' scattering amplitude versus anisotropy displays a shallow asymmetric minimum at theta = 1. Compared with the existence of only four inelastic scattering modes in the isotropic (theta = 1 case, the present six modes illustrate the partial lifting of essential degeneracies. Some similar results may be inferred for the more general case having two anisotropy parameters and eight modes.