Magnetization plateaus in the antiferromagnetic Ising chain with single-ion anisotropy and quenched disorder

TL;DR

This study investigates how quenched disorder and crystal-field interactions influence magnetization plateaus in an antiferromagnetic spin-1 chain, revealing disorder-dependent changes in plateau structure at low temperatures.

Contribution

It introduces a transfer-matrix method to analyze the effects of quenched disorder on magnetization plateaus in antiferromagnetic chains, highlighting the impact of different disorder distributions.

Findings

Bernoulli disorder increases the number of magnetization plateaus.

Plateaus are linked to different ground states as magnetic field varies.

Gaussian disorder suppresses plateau structures with increasing width.

Abstract

We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal-field and of the width of the distributions. For the Bernoulli distribution, the number of plateaus increases, with respect to the uniform case (F. Litaiff, J. R. de Sousa, and N. S. Branco, Sol. St. Comm. {\bf 147}, 494 (2008)) and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears, as the width increases.