反铁磁体XXZ的双临界性之谜
The puzzle of bicriticality in the XXZ antiferromagnet
摘要：
重整化群理论预言，XXZ反铁磁体在沿易磁化Z轴的磁场中，在场-温度平面上，渐近地具有四临界相图或三相点。无论是实验还是蒙特卡罗模拟都不能得到这样的相图。相反，他们发现了一个双临界相图。在这里，这种差异得到解决：在概括了一个普遍存在的条件确定的四临界点，我们采用新的重整化组递归关系附近的各向同性固定点，利用群论的考虑，并在三维使用准确的指数。这些表明，实验和模拟结果只能被理解，如果他们的轨迹流向波动驱动的一阶转变（和相关的三相点），但达到这个限制，只有过大的系统尺寸或相关长度。在交叉区域，人们期望一个双临界相图，因为确实是观察到的。类似的情况可以解释在其他各种具有竞争序参量的相图中，模拟和重整化群预测之间令人困惑的差异。
英文摘要：
Renormalization-group theory predicts that the XXZ antiferromagnet in a magnetic field along the easy Z-axis has asymptotically either a tetracritical phase-diagram or a triple point in the field-temperature plane. Neither experiments nor Monte Carlo simulations procure such phase diagrams. Instead, they find a bicritical phase-diagram. Here this discrepancy is resolved: after generalizing a ubiquitous condition identifying the tetracritical point, we employ new renormalization-group recursion relations near the isotropic fixed point, exploiting group-theoretical considerations and using accurate exponents at three dimensions. These show that the experiments and simulations results can only be understood if their trajectories flow towards the fluctuation-driven first order transition (and the associated triple point), but reach this limit only for prohibitively large system sizes or correlation lengths. In the crossover region one expects a bicritical phase diagram, as indeed is observed. A similar scenario may explain puzzling discrepancies between simulations and renormalization-group predictions for a variety of other phase diagrams with competing order parameters.
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