Phase transitions of Ising ferromagnets with nearest-neighbor ferromagnetic exchange interactions and competing biquadratic exchange interactions on a square lattice are investigated using a Monte Carlo method for spin values S=1, 3/2, 2, and 5/2. We find that for all the spin values studied in this paper, there always exists a transition line for each spin value in the high-temperature region. However, in the lower-temperature region, different transition behavior may occur for different spin values. In the T-K plane, a line running within the ordered phase, along the nonzero temperature region from T=0 and K/J=-1/3 to T=0 and K/J=-1.0 for spin S=3/2 and from T=0 and K/J=-1/6 to T=0 and K/J=-1/3 for spin S=2, separates the region of equal sublattice magnetizations from that of unequal sublattice magnetizations. For spin value S=5/2, two low-temperature lines in the T-K plane separate the region of equal sublattice magnetizations from that of unequal sublattice magnetizations with the one line running in the nonzero temperature region from T=0 and K/J=-0.1 to T=0 and K/J=-1/6 and the other line running from T=0 and K/J=-1/3 to T=0 and K/J=-1.0. A comparison with other approximate techniques is also made.

• Received 27 June 1994

DOI:https://doi.org/10.1103/PhysRevB.51.3605