Reentrant Phenomena in an Antiferromagnetic Ising Nanoparticle and a Ladder-Type Ising System under an Applied Transverse Field

Abstract

The phase diagrams and magnetization curves of antiferromagnetic nanoparticle and ladder-type system are investigated by using the effective-field theory with correlations. They have exhibited some characteristic features, such as the reentrant phenomena, when a finite transverse field h is applied and even when h = 0.0.

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Appendix

Appendix

The coefficients Kn and Ln (n = 1–3) in Eqs. (4) and (5) are given by the following:

$$ {K}_1=\frac{1}{4}\ \left[F\left(2.0\ J+{J}_{\mathrm{R}}\right)+F\left(2.0\ J-{J}_{\mathrm{R}}\right)\ \right] $$
$$ {K}_2=\frac{1}{4}\ \left[F\left(2.0\ J+{J}_{\mathrm{R}}\right)-F\left(2.0\ J-{J}_{\mathrm{R}}\right)+2.0\ F\left({J}_{\mathrm{R}}\right)\right] $$
$$ {K}_3=\frac{1}{4}\ \left[F\left(2.0\ J+{J}_{\mathrm{R}}\right)-F\left(2.0\ J-{J}_{\mathrm{R}}\right)-2.0\ F\left({J}_{\mathrm{R}}\right)\right] $$

and

$$ {L}_1=\frac{1}{4}\ \left[G\left(2.0\ J+{\mathrm{J}}_{\mathrm{R}}\right)+G\left(2.0\ J-{J}_{\mathrm{R}}\right)+2.0\ G\left({J}_{\mathrm{R}}\right)\ \right] $$
$$ {L}_2=\frac{1}{4}\ \left[G\left(2.0\ J+{J}_{\mathrm{R}}\right)+G\left(2.0\ J-{\mathrm{J}}_{\mathrm{R}}\right)-2.0\ G\left({J}_{\mathrm{R}}\right)\ \right] $$
$$ {L}_3=\frac{1}{4}\ \left[G\left(2.0\ J+{J}_{\mathrm{R}}\right)-G\left(2.0\ J-{J}_{\mathrm{R}}\right)\right]. $$

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Kaneyoshi, T. Reentrant Phenomena in an Antiferromagnetic Ising Nanoparticle and a Ladder-Type Ising System under an Applied Transverse Field. J Supercond Nov Magn 32, 3191–3200 (2019). https://doi.org/10.1007/s10948-019-5087-3

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Keywords

  • Phase diagrams
  • Magnetizations
  • Reentrant phenomena
  • Nanoparticle
  • Ladder-type system