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Ground State Properties of Ising Chain with Random Monomer–Dimer Couplings

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Abstract

We study analytically the one-dimensional Ising model with a random binary distribution of ferromagnetic and antiferromagnetic exchange couplings at zero temperature. We introduce correlations in the disorder by assigning a dimer of one type of coupling with probability x, and a monomer of the other type with probability \(1-x\). We find that the magnetization behaves differently from the original binary model. In particular, depending on which type of coupling comes in dimers, magnetization jumps vanish at a certain set of critical fields. We explain the results based on the structure of ground state spin configuration.

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Acknowledgments

We would like to thank Bernard Derrida for illuminating discussion and pointing out the possibility of flipping a combination of clusters at the critical fields. We also thank Ehsan Khatami for critical reading of the manuscript.

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Correspondence to Reza Sepehrinia.

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Ardebili, S.B.S., Sepehrinia, R. Ground State Properties of Ising Chain with Random Monomer–Dimer Couplings. J Stat Phys 163, 568–575 (2016). https://doi.org/10.1007/s10955-016-1499-7

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  • DOI: https://doi.org/10.1007/s10955-016-1499-7

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