Abstract
The low-density linked-cluster expansion of the free energy of the ferromagnetic Ising model with single-ion anisotropy, i.e., the term, is given by , with , , and . This is a low-temperature expansion with each spin having magnitude one. The sixth-order series available in the literature is analyzed by evaluating the zeros of as a function of , and from that the critical temperature is deduced. The knowledge of the critical temperature as a function of the anisotropy leads to the second-order part of the phase boundary of with which estimates a tricritical value of . The asymptotic behavior of is studied and from that the critical exponent of the isotherm as is found. It is observed that the anisotropy determines the transition temperature, but the exponent is independent of the same as expected from the universality hypothesis.
- Received 18 April 1979
DOI:https://doi.org/10.1103/PhysRevB.21.3971
©1980 American Physical Society