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A revisit to the Ising model in a transverse and random magnetic field

Author

Listed:
  • Souza, Itacy J.
  • Arruda, Paulo H.Z.
  • de Arruda, Alberto S.
  • Karimou, Mounirou
  • Tunes, Thiago M.
  • de Arruda, Marcelo F.Z.

Abstract

In this article we consider a Hamiltonian representing the Ising model in a random transverse magnetic field (RTIM). We use mean field theory via Bogoliubov’s inequality to calculate the Gibbs free energy and the longitudinal (mz) and transverse (mx) magnetizations. We show a quantum phase transition at zero temperature, i.e. the magnetization mz goes to zero only due to the transverse magnetic field. The temperature behavior as a function of the transverse magnetic field is also shown for different values of the anisotropy parameter p, where no tricritical behavior is observed. The behavior of mz and mx as a function of temperature and transverse magnetic field have been plotted, showing that there is no tricritical behavior.

Suggested Citation

  • Souza, Itacy J. & Arruda, Paulo H.Z. & de Arruda, Alberto S. & Karimou, Mounirou & Tunes, Thiago M. & de Arruda, Marcelo F.Z., 2023. "A revisit to the Ising model in a transverse and random magnetic field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    • Handle: RePEc:eee:phsmap:v:632:y:2023:i:p1:s0378437123008506
    DOI: 10.1016/j.physa.2023.129295
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