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physica status solidi (b)

Isothermal and Frequency‐Dependent Perpendicular Susceptibilities of the One‐Dimensional Ising Model with Nearest and Next‐Nearest Neighbour Interactions

L.L. Gonçalves

Published Apr 1, 1981• 0 citations
Publisher

Abstract

Abstract Exact expressions for the isothermal and frequency‐dependent perpendicular susceptibilities are obtained for the Ising model (s = 1/2) with nearest and next‐nearest neighbour interactions under zero external field. The static correlations are obtained by mapping the model in a pseudo Ising model with nearest‐neighbour interactions under an external field. The difference between the isothermal and isolated susceptibilities is discussed.

DOI
10.1002/pssb.2221040212

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Abstract Exact expressions for the isothermal and frequency‐dependent perpendicular susceptibilities are obtained for the Ising model (s = 1/2) with nearest and next‐nearest neighbour interactions under zero external field. The static correlations are obtained by mapping the model in a pseudo Ising model with nearest‐neighbour interactions under an external field. The difference between the isothermal and isolated susceptibilities is discussed.
Exact, closed expressions are obtained for the perpendicular and parallel susceptibilities of the one-dimensional spin-1/2 Ising model (i) with nearest neighbor interactions in a uniform magnetic field and (ii) with next-nearest neighbor interactions but without the magnetic field, in the thermodynamic limit. Graphs of the susceptibilities as a function of temperature for various magnetic field strengths in (i), and as a function of different ratios of the interaction strengths in (ii), are discussed.
The Kubo linear response theory is applied to the quantum mechanical Ising model to obtain a general expression which is valid for all regular lattices for the perpendicular response function in terms of spin correlations. For the honeycomb and the square lattices, exact expressions are found for the frequency-dependent initial perpendicular susceptibility, [Formula: see text] valid for all temperatures. For the honeycomb lattice, the present result for zero frequency agrees with Fisher's static calculation, whereas there is disagreement in the case of the square lattice. The discrepancy is resolved by using an extended calculation which explicitly illustrates the difference between isothermal and adiabatic susceptibilities.