The initial static transverse susceptibility is calculated for a double Ising chain whose Hamiltonian is invariant relative to the simultaneous reflection of all spins. The possibility is also noted of finding the imaginary part of the transverse dynamic susceptibility that governs the form of the magnetic resonance spectrum.
The dynamics of an Ising system is studied assuming that a microwave radiation field is coupled to the magnetic system through the transverse spin components. The transverse dynamic susceptibility is calculated with the use of the Green-function formalism in an exact manner, without the use of any decoupling scheme. The method yields an exact eigenvalue equation for the resonance frequencies, valid for any dimension and lattice, and a physical meaning of these resonances can be given in terms of the low-lying excitations for an Ising system. Those excitations correspond to spin-flip transitions in elementary clusters which represent all the possible spin arrangements of nearest neighbors. The present method does not allow for a calculation of line intensities without the help of statistical mechanics to evaluate correlation functions.
We study the transverse susceptibility of the fully frustrated antiferromagnetic Ising Δ-chain, extending Minami's transfer-matrix method to the transverse susceptibility of general-type Ising linear-chains [J. Phys. Soc. Jpn. 67 (1998), 2255]. For the transverse fields Γ1 in tip spin sites and Γ2 in bottom spin sites, we calculate zero-field transverse susceptibilities χxtip = lim Γ1 →0Mxtip/Γ1 and χxbottom = lim Γ2 →0Mxbottom/Γ2 while keeping the ratio Γ1/Γ2 fixed, where Mxtip (bottom) denotes the magnetization for tip (bottom) spin sites. Both the transverse susceptibilities follow Curie's law at low temperatures. We also calculate χxbottom(Γ1 > 0), the transverse susceptibility of the bottom spin chain under a finite tip-spin transverse field, to understand the Curie-type behavior in zero-field susceptibility. Using the second-order perturbation theory, we also discuss the Γ1 dependence of χxbottom (Γ1) at zero temperature.