Critical behaviors of transverse Ising ferromagnet with random bond and random longitudinal magnetic field

The transverse Ising model with bimodal random bond dilution and trimodal random longitudinal magnetic field was studied in terms of the effective-field theory (EFT) with correlations for a finite-cluster. The nearest-neighbor spins are assumed to be interacting randomly either ferromagnetically with probability p or the interaction between them are turned off with probability (1-p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1-p)$$\end{document}. It is also assumed that half of the spins are under the influence of longitudinal magnetic field with equal probability t/2 along z-axis having the values of +H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+H$$\end{document} and -H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-H$$\end{document} while the other half of spins is free of H with probability 1-t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-t$$\end{document}. The effects of changing the probabilities p and t, and the magnitudes of transverse and longitudinal magnetic fields for the magnetization components under temperature variations were examined in detail to obtain the possible phase diagrams of the model. It was obtained that the model exhibits both second- and first-order phase transitions, in addition to the tricritical points and reentrant behaviors for the first- and second-order phase transition temperature lines.