Critical properties of the spin-1 Blume–Capel model with a random transverse crystal field

© 2021 Elsevier B.V.The random transverse crystal field (RTCF) chosen to be along the x-axis is applied to the spin-1 Blume–Capel (BC) model and the mean-field approximation (MFA) is employed to investigate the behaviors of order-parameters and to obtain its phase diagrams. The selected form of the RTCF is in a bimodal form which is either turned on with probability p or turned off with 1−p on the sites of spin-1. The effects of the longitudinal and transverse crystal fields, i.e. Dz and Dx respectively, number of nearest-neighbors (NN) q, bilinear exchange interaction parameter J between the NN spins along the z-axis and temperature are analyzed in detail. The emphasis is given to the square lattice with q=4. It is found that the model displays first- and second-order phase transitions with the existence of tricritical point (TCP), critical end-points (CEP) and end-points (EP)