Spin-wave excitations and perpendicular susceptibility of a diluted antiferromagnet near percolation threshold

The long-wavelength excitations of a diluted antiferromagnet near the percolation threshold $p_c$ are studied. Within the hydrodynamic theory, the excitation frequency depends on two parameters, A and ${\chi }_t$. A is the stiffness associated with the spatial variation in the staggered magnetization and ${\chi }_t$ is the perpendicular susceptibility in the ordered state of the antiferromagnet. The critical behavior of A near $p_c$ is known. We develop a field-theoretic formalism to calculate ${\chi }_t$. We ex- plicitly calculate ${\chi }_t$ in the mean-field approximation and find that it diverges as ‖ln(p-$p_c$)‖, as the concentration p approaches $p_c$. Some further scaling arguments yield a scaling relation relating the divergence exponent of ${\chi }_t$ with other known exponents at the percolation critical point.