Baek Seung Ki, Mäkelä Harri, Minnhagen Petter, Kim Beom Jun
School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012125. doi: 10.1103/PhysRevE.88.012125. Epub 2013 Jul 19.
It is well known that the q-state clock model can exhibit a Kosterlitz-Thouless (KT) transition if q is equal to or greater than a certain threshold, which has been believed to be five. However, recent numerical studies indicate that helicity modulus does not vanish in the high-temperature phase of the five-state clock model as predicted by the KT scenario. By performing Monte Carlo calculations under the fluctuating twist boundary condition, we show that it is because the five-state clock model does not have the fully continuous U(1) symmetry even in the high-temperature phase while the six-state clock model does. We suggest that the upper transition of the five-state clock model is actually a weaker cousin of the KT transition so that it is q≥6 that exhibits the genuine KT behavior.
众所周知，如果q等于或大于某个阈值，q态时钟模型可以表现出Kosterlitz-Thouless（KT）转变，人们一直认为该阈值为5。然而，最近的数值研究表明，在五态时钟模型的高温相中，螺旋度模量并不像KT情景所预测的那样消失。通过在波动扭转边界条件下进行蒙特卡罗计算，我们表明这是因为五态时钟模型即使在高温相中也不具有完全连续的U(1)对称性，而六态时钟模型则具有。我们认为，五态时钟模型的上转变实际上是KT转变的一个较弱的变体，因此是q≥6时才表现出真正的KT行为。
