We provide a unified, comprehensive treatment of all operators that contribute to the antiferromagnetic, ferromagnetic, and charge-density-wave structure factors and order parameters of the hexagonal Hubbard Model. We use the Hybrid Monte Carlo algorithm to perform a systematic, carefully controlled analysis in the temporal Trotter error and of the thermodynamic limit. We expect our findings to improve the consistency of Monte Carlo determinations of critical exponents. We perform a data collapse analysis and determine the critical exponent $\beta =0.898\left(37\right)$ for the semimetal-Mott insulator transition in the hexagonal Hubbard Model. Our methods are applicable to a wide range of lattice theories of strongly correlated electrons.

中文翻译：

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蜂窝晶格上哈伯德模型中量子相变的反铁磁特性

我们对所有对六边形哈伯德模型的反铁磁、铁磁和电荷密度波结构因子和阶参数有贡献的算子进行了统一、全面的处理。我们使用混合蒙特卡罗算法对时间 Trotter 误差和热力学极限进行系统的、仔细控制的分析。我们希望我们的发现能够提高临界指数蒙特卡罗确定的一致性。我们执行数据崩溃分析并确定关键指数$\beta =0.898\left(37\right)$六边形哈伯德模型中的半金属-莫特绝缘体转变。我们的方法适用于广泛的强相关电子的晶格理论。