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

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.