Abstract:

By using a cutting approximation, the phase diagrams of the spin 1 random crystal field Blume-Capel (BCM) model is investigated for a cubic lattice. We discuss in detail the influence of random crystal field concentration and crystal field ratio on the phase diagram. The effect of four kinds of the random crystal field on the phase diagrams is discussed: distribution of diluted crystal field, distribution of positive and negative symmetry crystal field, distribution of positive and negative non-symmetry crystal field and distribution of random negative crystal field, and phase diagrams are given. Under crystal field dilution condition, the tricritical point (TCP) exists in a range of crystal field concentration, and, phase diagrams show reentrant phenomenon and crystal field degeneration pattern. Choosing crystal field ratio  α=-1.0 and α=-0.4, the range of crystal field concentration existed TCP is extended. Phase diagrams appear positive crystal field distribution. In particular, Choosing α=0.4, TCP exists over all crystal field concentration, reentrant phenomenon and crystal field degeneration pattern disappear, the phase transition lines have no meeting point with crystal axis and D→∞. And, the range of magnetic order phase reduces.

Key words:  Blume-Capel model; tricritical point; phase diagram