标题： 对平方格子上 q 状态铁磁 Potts 模型的债券加权张量重正化群研究 显示英文标题

标题： A Bond weighted tensor renormalization group study of the q-state ferromagnetic Potts models on the square lattice

摘要： 已知严格地，平方格子上$q$状态铁磁 Potts 模型的相变对于$q=4$是二阶的。 尽管如此，$q=4$模型的一些可观测量表现出一阶相变的特征。 例如，该模型的 Binder 比率$Q_2$的量出现负峰。 这种$Q_2$的非单调行为通常是相共存的结果，因此作为一阶相变的信号。 特别是，负峰应随着系统尺寸$L$的平方发散。 由于所述发散现象在四状态 Potts 模型中未被观察到，因此该模型的一阶相变场景被排除。 有趣的是，最近对四状态 Potts 模型的大规模蒙特卡罗研究观察到，当$L$增加时，能量密度分布的双峰结构变得更加明显。 这一发现表明，相共存信号随着$L$的增加而变得更加强烈。 由于这些异常的临界行为，我们在这里使用键加权张量重正化群（BWTRG）技术研究了平方格子上四状态 Potts 模型的能量密度$E$和比热$C_v$。 为了进行比较，同样使用相同的方法研究了平方格子上的$q=2$和$q=5$铁磁 Potts 模型。 值得注意的是，我们的结果暗示$q=4$模型可能存在一个小能隙。 虽然提到的小能隙的出现可以合理解释，并且随着更深入的研究会消失，但我们的发现表明，是否一阶相变的信号是真实的还是人工效应，需要进一步和详细的研究。 显示英文摘要

摘要： It is known rigorously that the phase transition of the $q$-state ferromagnetic Potts model on the square lattice is second order for $q=4$. Despite this fact, some observables of the $q=4$ model show features of a first-order phase transition. For example, negative peak appears for the quantity of Binder ratio $Q_2$ of this model. Such a non-monotonic behavior of $Q_2$ is typically a consequence of phase coexistence, hence is served as a signal of a first-order phase transition. In particular, the negative peak should diverge with linear system size $L$ squared. Since the mentioned divergence phenomenon is not observed for the 4-state Potts model, the scenario of a first-order phase transition for this model is ruled out. Interestingly, a recent large scale Monte Carlo investigation of the 4-state Potts model observes that the two-peak structure of the energy density distribution becomes more noticeable when $L$ increases. This finding indicates the signal of coexistence of phases is getting stronger with $L$. Due to these unusual critical behaviors, here we study the energy density $E$ and the specific heat $C_v$ of the 4-state Potts model on the square lattice using the technique of bond weighted tensor renormalization group (BWTRG). For a comparison purpose, $q=2$ and $q=5$ ferromagnetic Potts models on the square lattice are investigated using the same method as well. Remarkably, our results do imply there may be a small energy gap for $q=4$ model. While the appearance of the mentioned small energy gap can be explained plausibly and it will disappear with a more sophisticated investigation, our finding suggests that whether a message of a first-order phase transition is genuine or is an artificial effect requires further and detailed investigations.