Series expansions for a generalized XY hamiltonian: II. Tricritical behaviour of the Takagi model

The high-temperature series expansions for the square of the fluctuation in the order parameter, for the specific heat, the concentration and the concentration susceptibility for the Takagi model on an f.c.c. lattice are analysed in the field variables. We obtain for the critical exponent $\text{γ =}\text{4}\text{3}$ and the specific heat is possibly logarithmically divergent. If we take the tricritical point to be determined by γ_t = 1, the tricritical exponents α_t, λ_t and ω_t are found to be consistent with $\text{1}\text{2}$.