Journal of Physics C Solid State Physics

Transverse susceptibility in spin S Ising chains

Michael F. Thorpe, M. F. Thomsen

Published Mar 20, 1983• 13 citations

Abstract

It is shown that the transverse susceptibility of a one-dimensional spin S Ising system can be calculated by combining linear response theory with the transfer matrix technique. Closed form expressions for infinite chains are obtained for S= 1 / 2 and S=1, and numerical results are displayed for S= 1 / 2 to S= 5 / 2 .

DOI: 10.1088/0022-3719/16/8/004

Related papers

The zero-field susceptibility of the transverse Ising chain with arbitrary spin

Kazuhiko Minami

The zero-field susceptibility of the transverse Ising chain with arbitrary spin-S is expressed in terms of the eigenvector for the maximum eigenvalue of its transfer matrix. As a result, the exact susceptibility is explicitly obtained for , 1, and can be obtained at least for . The numerical calculations of the susceptibility for arbitrary spin are possible and those for S = 6, 12 and 24 are given. It is also derived that the zero-temperature limit of the susceptibility is independent on spin-S.

Journal of Physics A Mathematical and GeneralOct 7, 199611 citations

The Exact Susceptibility of the Spin-S Transverse Ising Chain with Next-nearest-neighbor Interactions

Kazuhiko Minami

The zero-field susceptibility of the spin-S transverse Ising chain with next-nearest-neighbor interactions is obtained exactly. The susceptibility is given in an explicit form for S=1/2, and expressed in terms of the eigenvectors of the transfer matrix for general spin S. It is found that the low-temperature limit is independent of spin S, and is divergent at the transition point.

arXiv:2212.12693Journal of the Physical Society of JapanApr 14, 20231 citation

Longitudinal and Transverse Susceptibilities of the One-Dimensional Ising Model with Competing Interactions

Isao Harada

Exact expressions for the wave-number dependent longitudinal and transverse susceptibilities of the one-dimensional Ising model with competing interactions are obtained by combining the linear response theory with the transfer matrix method. The longitudinal susceptibility exhibits a characteristic wave-number dependence, while the transverse susceptibility is independent of wave-number. Special attention is paid to the condition under which the longitudinal susceptibility has a maximum value at nonzero wave-number. Furthermore, the phase diagram of a system with weakly coupled Ising chains is considered in connection with the one-dimensional susceptibility.

Journal of the Physical Society of JapanDec 1, 198317 citations

Crystal-field effect on the transverse susceptibility in spin-SIsing chains

Ibha Chatterjee

The crystal-field effect in the one-dimensional Ising model for spins S=1 to (5/2) has been studied in linear-response theory by considering its effect on the susceptibility in transverse directions. For S=1 analytical expressions are obtained, and for higher spins numerical calculations are performed for various values of the crystal-field parameter (D) and the exchange parameter (J). It has been found that the susceptibility maxima which appear for D<2J, do not occur for D>2J.

Physical review. B, Condensed matterDec 1, 19864 citations

An Exact Calculation of the Transverse Susceptibility for an Antiferromagnetic Ising Chain

N. Kunisada, Y. Fukumoto

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.

arXiv:0712.4306Progress of Theoretical PhysicsJun 1, 20081 citation

Dilute Ising chains with spin S

M. F. Thomsen, Michael F. Thorpe

Randomly diluted one-dimensional Ising chains of spin S are studied by breaking the systems down to noninteracting finite segments. Exact closed-form expressions are obtained for the specific heat and perpendicular susceptibility of S= 1 / 2 chains and numerically exact results are given for spins up to 5 / 2 .

Journal of Physics C Solid State PhysicsJul 30, 19837 citations