论文标题
三态POTTS模型的上部临界维度
Upper critical dimension of the 3-state Potts model
论文作者
论文摘要
我们考虑$ d \ geq2 $尺寸中的三州potts型号。对于$ d $，小于临界尺寸$ d_ \ text {crit} $的$ d $，该模型具有关键和三个固定点。在$ d = 2 $中，这些固定点由最小型号描述，因此可以解决。但是，对于$ d> 2 $，强耦合使它们难以学习，并且就$ d_ \ text {crit} $的值尚无共识。我们使用数值共形性启动程序来计算一般$ d $的关键和三个固定点的关键指数。在$ d = 2 $中，我们的结果与预期值相匹配，随着我们增加$ d $，我们发现每个固定点的关键指数越来越近，直到它们合并在$ d_ \ text {crit} \ lyssim 2.5 $附近。
We consider the 3-state Potts model in $d\geq2$ dimensions. For $d$ less than the upper critical dimension $d_\text{crit}$, the model has a critical and a tricritical fixed point. In $d=2$, these fixed points are described by minimal models, and so are exactly solvable. For $d>2$, however, strong coupling makes them difficult to study and there is no consensus on the value of $d_\text{crit}$. We use the numerical conformal bootstrap to compute critical exponents of both the critical and tricritical fixed points for general $d$. In $d=2$ our results match the expected values, and as we increase $d$ we find that the critical exponents of each fixed point get closer until they merge near $d_\text{crit}\lesssim 2.5$.
