Tests of strong scaling in the three-dimensional Ising model

Abstract

We study numerically the amplitudes $E^{\pm }\left(\overrightarrow{\mathrm{R}}\right)$ of the ${\left|\frac{\Delta T}{T_c}\right|}^{1-\alpha }$ variation in the spin-spin correlation functions $〈s_{\overrightarrow{0}}{s}_{\overrightarrow{\mathrm{R}}}〉$, of three-dimensional Ising models in zero field above and below $T_c$. By allowing for reasonable correction terms to the asymptotic behavior $E^{\pm }\left(\overrightarrow{\mathrm{R}}\right)\approx E_0^{\pm }{\left(\frac{R}{a}\right)}^{\zeta }$, where $a$ is the lattice spacing, we find consistency with the strong-scaling prediction $\zeta =\frac{(1-\alpha )}{\nu }-d+2-\eta \simeq 0.31$, and reasonable agreement with universality and $\epsilon$-expansion estimates of the amplitudes $E_0^{\pm }$.