An exact calculation of the transverse susceptibility for an antiferromagnetic Ising Δ chain

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. For the transverse fields Γ1 in tip spin sites and Γ2 in bottom spin sites, we calculate zero-field transverse susceptibilities χtipx=limΓ1→0 Mtipx/Γ1 and χ.bottomx=limΓ2→0 Mbottomx/Γ2 while keeping the ratio Γ1/Γ2 fixed, where Mtip(bottom)x denotes the magnetization for tip (bottom) spin sites. Both the transverse susceptibilities follow Curie's law at low temperatures. We also calculate χbottomx(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 χbottomx(Γ1) at zero temperature. (author)