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Physica A Statistical Mechanics and its Applications

Nonuniform effective temperatures in Ising models on tangled chains

J.C. Lee, J.M. Stephens, Lawrence R. Mead, R.F. Joyce

Published Sep 1, 1990• 3 citations
Publisher
DOI
10.1016/0378-4371(90)90289-5

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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 a l o n g the chain is somewhat as a "transition region" condition for this behaviour.Our results indicate also the existence of nonzero entropy at zero temperature.

Acta Physica Polonica A•Jun 1, 1994•3 citations

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Ising Model on Tangled Chain. II. Magnetization and Susceptibility

Rexhep Mejdani

In the preceding paper we have considered an Ising model defined on tangled chain to study the behaviour of the free energy and entropy, particul ar l y i n t he zer o-f i el d and zer o-t emper at ur e l i mi t .I n t hi s paper , f ol l owi ng 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.

Acta Physica Polonica A•Jun 1, 1994•0 citations
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 a l o n g the chain is somewhat as a "transition region" condition for this behaviour.Our results indicate also the existence of nonzero entropy at zero temperature.
In the preceding paper we have considered an Ising model defined on tangled chain to study the behaviour of the free energy and entropy, particul ar l y i n t he zer o-f i el d and zer o-t emper at ur e l i mi t .I n t hi s paper , f ol l owi ng 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.