论文标题
三个维度的双智力相图
Bi- and tetracritical phase diagrams in three dimensions
论文作者
论文摘要
许多物理系统的关键行为涉及两个竞争的$ n^{} _ 1- $和$ n^{} _ 2- $ component订单 - parameters，$ {\ bf s}^{} _ 1 $和$ {\ bf s}^{}^{}^{}^{} _ 2 $，$改变外部控制参数$ g $，％（例如单轴压力或磁场），一个遇到$ {\ bf s}^{}^{} _ 1 $下方的订购，$ g <0 $和$ g <0 $和$ {\ bf s}} _ 2 $ for $ g <0 $ for $ g <0 $ for $ g <0 $ for $ g <0 $ for $ g <0 $ for $ g <0 $ for $ g <0这两个有序阶段通过一阶线隔开，该线路符合上述临界线，或者在两种临界线上符合两种临界线的中间（混合）相位，这些临界线符合上述临界线。对于$ n = 1+2 = 3 $，（Bi-bi-或tetra-）多政治点周围的临界行为要么属于非旋转不变的（立方或双色的）固定点的通用类别，要么具有波动驱动的一阶过渡。这些渐近行为仅非常接近过渡。我们提出准确的重归化组流量轨迹，从而在多政治上产生有效的跨界指数。
The critical behavior of many physical systems involves two competing $n^{}_1-$ and $n^{}_2-$component order-parameters, ${\bf S}^{}_1$ and ${\bf S}^{}_2$, respectively, with $n=n^{}_1+n^{}_2$. Varying an external control parameter $g$, %(e.g. uniaxial stress or magnetic field), one encounters ordering of ${\bf S}^{}_1$ below a critical (second-order) line for $g<0$ and of ${\bf S}^{}_2$ below another critical line for $g>0$. These two ordered phases are separated by a first-order line, which meets the above critical lines at a bicritical point, or by an intermediate (mixed) phase, bounded by two critical lines, which meet the above critical lines at a tetracritical point. For $n=1+2=3$, the critical behavior around the (bi- or tetra-) multicritical point either belongs to the universality class of a non-rotationally invariant (cubic or biconical) fixed point, or it has a fluctuation driven first-order transition. These asymptotic behaviors arise only very close to the transitions. We present accurate renormalization-group flow trajectories yielding the effective crossover exponents near multicriticality.
