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We obtain the complete phase diagram of the antiferromagnetic $J_{1}$-$J_{2}$model, $0\leq \alpha = J_2/J1 \leq 1$, within the framework of the $O(N)$nonlinear sigma model. We find two magnetically ordered phases, one with N\'eel order, for $\alpha \leq 0.4$, and another with collinear order, for$\alpha\geq 0.6$, separated by a nonmagnetic region, for $0.4\leq \alpha \leq0.6$, where a gapped spin liquid is found. The transition at $\alpha=0.4$ is ofthe second order while the one at $\alpha=0.6$ is of the first order and thespin gaps cross at $\alpha=0.5$. Our results are exact at $N\rightarrow\infty$and agree with numerical results from different methods.

Magnetic quantum phase transitions of the antiferromagnetic J_{1}-J_{2} Heisenberg model