An Exact Calculation of the Transverse Susceptibility for an Antiferromagnetic Ising Δ Chain(Condensed Matter and Statistical Physics)

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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 Γ_1 in tip spin sites and Γ_2 in bottom spin sites, we calculate zero-field transverse susceptibilities χ^x_<tip>=lim_<Γ_1→_0>M^x_<tip>/Γ_1 and χ^x_<bottom>=lim_<Γ_2→0>M^x_<bottom>/Γ_2 while keeping the ratio Γ_1/Γ_2 fixed, where M^x_<tip(bottom)> denotes the magnetization for tip (bottom) spin sites. Both the transverse susceptibilities follow Curie's law at low temperatures. We also calculate χ^x_<bottom>(Γ_1>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 Γ_1 dependence of χ^x_<bottom>(Γ_1) at zero temperature.
2008-06-25