Ising Model on Tangled Chain. I. Free Energy and Entropy
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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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