Department of Physics, Soongsil University, Seoul 06978, Korea and Institute for Integrative Basic Sciences, Soongsil University, Seoul 06978, Korea.
Phys Rev E. 2017 Dec;96(6-1):062105. doi: 10.1103/PhysRevE.96.062105. Epub 2017 Dec 5.
Quantum phase transitions of a q-state Potts model in fractal lattices are studied using a continuous-time quantum Monte Carlo simulation technique. For small values of q, the transition is found to be second order and critical exponents of the quantum critical point are calculated. The dynamic critical exponent z is found to be greater than one for all fractals studied, which is in contrast to integer-dimensional regular lattices. When q is greater than a certain value q_{c}, the phase transition becomes first order, where q_{c} depends on the lattice. Further analysis shows that the characteristics of phase transitions are more sensitive to the average number of nearest neighbors than the Hausdorff dimension or the order of ramification.
使用连续时间量子蒙特卡罗模拟技术研究了分形格子上 q 态 Potts 模型的量子相变。对于小的 q 值，发现相变是二级的，并计算了量子临界点的临界指数。发现所有研究的分形上的动态临界指数 z 都大于 1，这与整数维正则格子相反。当 q 大于某个值 q_c 时，相变变为一级，其中 q_c 取决于格子。进一步的分析表明，相变的特征对平均最近邻数的敏感性比对豪斯多夫维数或分支阶数更敏感。
