本文对于二维Clock Potts模型的相变和长程序做了详细的总结。q态Clock Potts模型在q≤4时具有一个单独相变，而对于q≥5则具有两个相变。蒙特卡洛模拟表明，五态Clock Potts模型的螺旋模量（q = 5） 不会在高温相变时消失。这与螺旋模量消失的q≥6的Clock Potts模型形成对照。 这意味着五态Clock Potts模型的相变不同于KT相变。以及在这种相变中的改变是由角度方向的多少和交互作用势之间的相互作用引起的：通过稍微修改交互作用势，q = 6的KT相变变成相同的非KT转变。 同样，当使用Villain势能时，对于q = 5，将恢复KT相变。
蒙特卡洛方法的基本思想就是，当人们想要求解的问题是某一个随机变量的期望值，或是某一种事件出现的概率时，它可以利用随机数的统计规律来进行模拟和计算，便得到这个随机变量的平均值，或这种事件出现的频率，并用其作为问题的解。
并且考虑到序参量的分布，提出一个可观测量使得能清晰分辨在二维的一般q态Clock Potts模型中真正的长程序和准长程序。通过对q=8的蒙特卡洛模拟测量这个量，构建了相图，并且确定了真正的长程序，准长程序和无序相的沿着相分离线的临界性质。结果表示只要两个相分离线合并就会出现不连续的order-disorder的相变的理论预测。这些研究对人们研究相变具有重要意义,对这些研究的总结增强了人们对于Clock Potts模型的认知，使人们对于相变研究的兴趣更加浓厚。

This article makes a detailed summary of the phase transition and long-range-order(LRO) of the 2D Clock Potts model. The q-state Clock model has a single phase transition when q≤4, and two phase transitions for q≥5. Monte Carlo simulations show that the helicity modulus of the five-state Clock model (q = 5) does not disappear when the phase transition appears at high temperature. It is in contrast to the Clock model with q≥6 where the helicity modulus disappears. This means that the phase transition of the five-state Clock model is different from the KT phase transition. And the change in this phase transition is caused by the interaction between the angular direction and the interaction potential: by slightly modifying the interaction potential, the KT transition at q = 6 becomes the same non-KT transition. Similarly, for q = 5, the KT transition is recovered by using Villain potential.
The basic idea of the Monte Carlo method is that when the problem is the probability of an event, or the expected value of a random variable, it can get the frequency of the event, or the average value of the random variable, and use it as a solution to the problem.
And considering the distribution of order parameters, an observable measurement is proposed to make it possible to distinguish true LRO from quasi-LRO in the 2D generalized q-state Clock model. By measuring this quantity with a Monte Carlo simulation of q = 8, a phase diagram was constructed, and the critical properties of true long LRO, quasi-LRO and disorder along the phase separation line were determined. The results indicate that the theoretical prediction of a discontinuous order-disorder transition will occur whenever the two phase separation lines merge. These studies are of great significance to the study of phase transitions in strongly correlated electronic systems. The summary of these studies enhances people's understanding of Clock Model and makes people more interested in phase transition study.