Borisenko O, Chelnokov V, Cortese G, Fiore R, Gravina M, Papa A, Surzhikov I
Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev, Ukraine.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051131. doi: 10.1103/PhysRevE.86.051131. Epub 2012 Nov 26.
We perform an analytical and numerical study of the phase transitions in three-dimensional Z(N) lattice gauge theories at finite temperature for N>4, exploiting equivalence of these models with a generalized version of the two-dimensional vector Potts models in the limit of vanishing spatial coupling. In this limit the Polyakov loops play the role of Z(N) spins. The effective couplings of these two-dimensional spin models are calculated explicitly. It is argued that the effective spin models have two phase transitions of BKT type. This is confirmed by large-scale Monte Carlo simulations. Using a cluster algorithm we locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices and compute the helicity modulus, the average action, and the specific heat. A scaling formula for the critical points with N is proposed.
我们对N>4时有限温度下三维Z(N)晶格规范理论中的相变进行了分析和数值研究，利用这些模型与二维矢量Potts模型广义版本在空间耦合消失极限下的等价性。在此极限下，Polyakov圈起着Z(N)自旋的作用。明确计算了这些二维自旋模型的有效耦合。论证了有效自旋模型具有BKT型的两个相变。大规模蒙特卡罗模拟证实了这一点。使用聚类算法，我们确定了临界点的位置，并详细研究了两个相变的临界行为。特别是，我们确定了各种临界指数，并计算了螺旋模量、平均作用量和比热。提出了一个关于临界点与N的标度公式。
