Crossover scaling functions for two-point correlations near tricritical points

The expectations of phenomenological crossover scaling theory are worked out for two-point correlation functions in zero field above the primary critical point. Renormalization-group recursion relations are then used to construct the two-point correlation function for the changeover from tricritical to critical-line behavior, above the tricritical point, to first order in $\epsilon =4-d$, for $3\le d<\mathrm{}4\mathrm{}$. An explicit expression is obtained for the normalized double-scaling function ${\hat{\Gamma }}_N(q^2{\xi }^2, \frac{g}{t^{\varphi }})$, for the general scaling variable $q^2{\xi }^2$, and the crossover variable $w=\frac{g}{t^{\varphi }}$, $q\ll a^{-1\mathrm{}}$ being the wave vector; $\xi \gg a$ is a second-moment correlation length and $a$ the lattice spacing. In the tricritical regime, $w\simeq 0$, ${\hat{\Gamma }}_N$ ($x^2, w$) has the Ornstein-Zernicke form and the changeover to the critical regime $w\simeq \infty$ is explicitly discussed. The limitation of the results, within our calculations to first order in $\epsilon$, are pointed out.