Sierpiński金字塔上的量子Potts模型

Critical behavior of the 3-state Potts model on Sierpinski carpet

We study the critical behavior of the 3-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations, for a Hausdorff dimension $d_{f}$ $\simeq 1.8928$. The phase transition is shown to be a second order one. The maxima of the susceptibility of the order parameter follow a power law in a very reliable way, which enables us to calculate the ratio of the exponents $γ/ν$. We find that the scaling corrections affect the behavior of most of the thermodynamical qu…

Potts模型在Sierpinski垫片和Hanoi格上的精确配分函数

Exact partition function of the Potts model on the Sierpinski gasket and the Hanoi lattice

本文基于图论和重整化群方法，推导了非整数维度的Sierpinski格和Hanoi格上Potts模型的精确配分函数方程，并通过Monte Carlo模拟和不动点分析揭示了Fisher零点位置与吸引域边界的关系。

Quantum criticality from Ising model on fractal lattices

We study the quantum Ising model on the Sierpiński triangle, whose Hausdorff dimension is $\log 3/ \log 2 \approx 1.585$, and demonstrate that it undergoes second-order phase transition with scaling relations satisfied precisely. We also study the quantum $3$-state Potts model on the Sierpiński triangle and find first-order phase transition, which is consistent with a prediction from $ε$-expansion that the transition becomes first-order for $D > 1.3$. We then compute critical exponents of the Ising model on higher-dimensional Sierpiński pyramids with various Hausdorff dimension via Monte-Carlo…

作为动力系统的自相似格点上 Potts 模型配分函数与多重相变

Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions

本文将 Sierpinski 垫片与 Hanoi 图等自相似格点上的 Potts 配分函数归约为动力系统，据此确定相图，并利用吸引域构造具有多个临界温度的格点。

具有可分解状态数的活性 Potts 模型的动态模式

Dynamic modes of active Potts models with factorizable numbers of states

本研究通过蒙特卡洛模拟发现，可分解状态数的活性 Potts 模型在特定接触能量下会出现跳跃状态和螺旋波等新动态模式，且转变标度指数偏离平衡值。