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Progress of Theoretical Physics

Exact Initial Transverse Susceptibility of a Mixed Spin Ising Chain

T. Kaneyoshi

Published Jul 1, 1997• 6 citations
Publisher

Abstract

The exact initial transverse susceptibility of a mixed spin Ising chain composed of alternating spin-1/2 and spin-S (S > 1/2) atoms has been obtained by a method based on both exact Ising spin identities and a differential operator technique. Numerical results are presented and discussed by selecting the two values S = 1 and S = 3/2.
DOI
10.1143/ptp.98.57

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The exact solutions of the spin-spin correlation functions, the internal energy and the specific heat in a mixed spin Ising chain made up of two kinds of alternating magnetic atoms, namely spin-1/2 atoms and spin-S (S > 1/2) atoms with a crystal-field interaction constant D, are derived by the use of Ising spin identities and a differential operator technique. These solutions are valid for arbitrary values of S and D. Some numerical results are given for the specific heat. We find that the results exhibit characteristic behavior which does not follow the Schottky-type when the value of D becomes smaller than a (negative) critical value.
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.