In the preceding paper we have considered an Ising model defined on tangled chain to study the behaviour of the free energy and entropy, particularly in the zero-field and zero-temperature limit. In this paper, following the main line and basing on some results of the previous work, we shall study in the "language" of state configurations the behaviour of the magnetization and the susceptibility for different conditions of the model, to understand better the competition between the ferromagnetic bonds along the chain and the antiferromagnetic additional bonds across the chain. Particularly interesting is the behaviour of the susceptibility in the zero-field and zero-temperature limit. Exact solutions for the magnetization and susceptibility, generated by analytical calculations and iterative algorithms, are described. The additional bonds, introduced as a form of perfect disorder, indicate a particular effect on the spin correlation. We found that the condition J = -J' between the ferromagnetic interaction J along the chain and the antiferromagnetic interaction J' across the chain is somewhat as a "transition-region" condition for this behaviour.
The semimetallic quasi-one-dimensional S=1/2 Heisenberg antiferromagnet Yb_{4}As_{3} was studied by low-temperature measurements of the specific heat C(T,B), thermal expansion α(T,B), and thermal conductivity ĸ(T,B). At finite magnetic fields (B≤12 T) we observed the following distinct anomalies: (1) the magnon contribution to C(T,0), γ T, with large coefficient γ ≈ 200 mJ/(K^{2}mol), becomes strongly reduced with field, and (2) a broad hump in C(T,B=const) is induced at slightly higher temperatures. (3) The latter corresponds to a pronounced peak in α(T,B=const) as well as (4) to a broad minimum in ĸ(T,B= const)/ĸ(T,0). These anomalies are well described by the classical sine-Gordon solution of a one-dimensional Heisenberg antiferromagnet with a weak easy-plane anisotropy. However, the soliton-rest energy deduced from the experimental results depends on the magnetic field like E_{S} ~ B^{ν}, with an exponent ν ≈ 0.66, while the classical sine-Gordon model requires ν=1. Thus, our results suggest an alternative description of soliton excitations in an antiferromagnetic S=1/2 Heisenberg chain in terms of the quantum sine-Gordon model, for which an exponent ν=2/3 is appropriate.
In this paper we have considered an Ising model defined on tangled chain, in which more bonds have been added to those of pure Ising chain. To understand their competition, particularly between ferromagnetic and antiferromagnetic bonds, we have studied, using the transfer matrix method, some simple analytical calculations and an iterative algorithm, the behaviour of the free energy and entropy, particularly in the zero-field and zero-temperature limit, for different configurations of the ferromagnetic tangled chain and different types of additional interactions (ferromagnetic or antiferromagnetic). We found that the condition J = -J' between the ferromagnetic interaction J along the chain and the antiferromagnetic interaction J' across the chain is somewhat as a "transition region" condition for this behaviour. Our results indicate also the existence of nonzero entropy at zero temperature.
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