Quantum tricriticality of a $J_1$-$J_2$ antiferromagnetic Ising model on asquare lattice is studied using the mean-field (MF) theory, scaling theory, andthe unbiased world-line quantum Monte-Carlo (QMC) method based on the Feynmanpath integral formula. The critical exponents of the quantum tricritical point(QTCP) and the qualitative phase diagram are obtained from the MF analysis. Byperforming the unbiased QMC calculations, we provide the numerical evidence forthe existence of the QTCP and numerically determine the location of the QTCP inthe case of $J_1=J_2$. From the systematic finite-size scaling analysis, weconclude that the QTCP is located at $H_{\rm QTCP}/J_1=3.260(2)$ and$\Gamma_{\rm QTCP}/J_1=4.10(5)$. We also show that the critical exponents ofthe QTCP are identical to those of the MF theory because the QTCP in this modelis in the upper critical dimension. The QMC simulations reveal thatunconventional proximity effects of the ferromagnetic susceptibility appearclose to the antiferromagnetic QTCP, and the proximity effects survive for theconventional quantum critical point. We suggest that the momentum dependence ofthe dynamical and static spin structure factors is useful for identifying theQTCP in experiments.
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