Tricritical behavior of the Blume-Capel model

The thermodynamic behavior of the fcc Blume-Capel ferromagnet, $H={-}J{Σ}{}{〈12〉}{S}ᶻ(1){S}ᶻ(2)+{Δ}{Σ}{}{1}{[{S}ᶻ(1)]}²{-}h{Σ}{}{1}{S}ᶻ(1), {S}ᶻ=0, ±{}1,$ is studied by series-extrapolation techniques. By using both high- and low-temperature series, we are able to trace first- and second-order branches of the phase boundary and examine behavior at temperatures both above and below the phase transition. We find a tricritical point at kBTₜ12J=0.2615±0.0070, Δₜ12J=0.4716±0.0010. Tricritical exponents are consistent with γₜ=γₜ^'=1, βₜ=1/4, φₜ=νₜ=αₜ=αₜ^'=1/2, in good agreement with tricritical mean-field theory and the Gaussian tricritical fixed point of Riedel and Wegner.