Critical properties of the biaxial Ising model with both the longitudinal crystal field and the transverse dilution crystal field

Within the effective field theory (EFT), the critical properties of the biaxial Ising model with both longitudinal crystal field and transverse dilution crystal field are investigated for a simple cubic lattice. The tricritical point (TCP) and its trajectory are discussed in T – D x and T – D z space. A new phenomenon of two TCPs is found in T – D x space. There exists a second-order line between two first-order lines, separated by two TCPs. The change of dilution concentration leads to a complex relation of the trajectory of the TCP. The degenerate patterns at the ground state appear by changing the longitudinal crystal field. The range of the ordered phase for transition lines labelled as a positive or (negative) value of D x / J becomes larger or (smaller) with the decrease of t x in T – D z space. Some results have not been revealed in previous works.