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We investigate the ground state of the $J_1$-$J_2$ spin-1/2 chain with$J_1<0$ and $J_2>0$ in the case that the nearest-neighbor $J_1$ interaction inthe $z$-direction has a weak anisotropy as $J_1 (1-\alpha)$. We perform aperturbational analysis for small $\alpha$ and $\lambda \equiv J_2- |J_1|/4$with the exact solution of the unperturbed ground state for $\alpha = \lambda =0$. The scaling property of the ground state energy is examined in detail. Bythe numerical diagonalization analysis of finite size systems, we found thephase boundary equation between the spin fluid and dimer phases as $\alpha_{\rmc} = 14 \lambda_{\rm c}^{4/3}$.

Scaling Property of the F-AF Spin Chain Near the Exactly Solvable Point