Critical behavior of spin-one three-dimensional Ising model with single-ion anisotropy

Abstract

The low-density linked-cluster expansion of the free energy of the ferromagnetic Ising model with single-ion anisotropy, i.e., the Δ ΣiS_zi² term, is given by -βf(βJ,βΔ,βh)=1/2qJ+h-Δ+Σl=1^∞(u¹²µ)^lL₁(u,η),with u=exp(-J/k_BT),µ=exp(-2mh/k_BT), and η =exp(Δ/k_BT). This is a low-temperature expansion with each spin S_i having magnitude one. The sixth-order series available in the literature is analyzed by evaluating the zeros of L˜_l=u^12lL_l as a function of Δ, 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 βJ with βΔ which estimates a tricritical value of Δ. The asymptotic behavior of L˜_l is studied and from that the critical exponent δ of the M-h isotherm as h→0 is found. It is observed that the anisotropy determines the transition temperature, but the exponent δ is independent of the same as expected from the universality hypothesis.