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Progress of Theoretical Physics

Thermodynamics of a Mixed Spin Ising Chain

T. Kaneyoshi

Published Mar 1, 1997• 15 citations
Publisher

Abstract

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.

DOI
10.1143/ptp.97.407

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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.
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The one-dimensional Ising model with arbitrary nearest neighbor interactions and a magnetic field is formulated in terms of the spin correlation function relations derived in the preceding article I. The local magnetization and the two-spin correlation functions are shown to satisfy a set of coupled algebraic summation equations. The solution of this set is given in terms of a power series in hyberbolic tangents of the magnetic field strength, for chains of arbitrary length. For cases in which the interaction constants are random variables, explicit expressions are derived for the configurational averaged magnetization and the two-spin correlation functions to the lowest order in the magnetic field.
A mixed Ising-Heisenberg spin system consisting of triangular XXZXXZXXZ-Heisenberg spin clusters assembled into a chain by alternating with Ising spins interacting to all three spins in the triangle is considered. The exact solution of the model is given in terms of the generalized decoration-iteration map and within the transfer-matrix technique. Exact expressions for thermodynamic functions are derived. Ground-state phase diagrams and thermodynamic and magnetic properties of the system are examined.
The one-dimensional spin-1/2 Ising-Heisenberg ferromagnets are studied by the Green's function method at finite temperatures. The Green's function is decoupled in terms of the correlation functions of 〈S0z{\mathit{S}}_{0}^{\mathit{z}}S0z​Snz{\mathit{S}}_{\mathit{n}}^{\mathit{z}}Snz​〉 and 〈S0+{\mathit{S}}_{0}^{+}S0+​${\mathit{S}}_{\mathit{n}}^{\mathrm{\ensuremath{-}}}$〉 under the constraint of 〈Sz{\mathit{S}}^{\mathit{z}}Sz〉=0, from which a set of self-consistent equations are derived and solved numerically. The thermodynamic properties such as internal energy, specific heat, and zero-field parallel susceptibility are calculated. Our results predict the correct behavior for the correlation functions and thermodynamic quantities in the entire temperature region, in agreement both with the exact numerical results on the finite chain and the experimental data.