复杂Sierpinski地毯上的Potts模型

POTTS MODEL ON COMPLEX SIERPINSKI CARPETS

考察了复杂Sierpinski地毯上Potts模型的相变与临界现象。给出了其连接性维数D_(con)和(?)_(con)的表达式,并讨论了临界指数随连接性维数(?)_(con)、分形维数D(D_(con))、连接度Q、空隙度L和Potts模型的自旋态数q的变化情况。结果表明存在一定规律性,(?)_(con),D和Q是表征分形的重要参量。还指出了Suzuki的不等式v(d)>v(d~′)(d<d~′)对d=min(D_(con),(?)_(con))是不成立的。

Rhase transitions and critical behaviours of the Ports model on some complex Sierpinski carpets are studied. The expressions of the connectivity dimensionality D_(con) and D_(con) are given for Sierpinski carpets. The variations of the critical exponents with varying connectivity Q, connectivity dimensionality D_(con) fractal dimensionality D(D_(con)), lacunarity L and the number of states of the Potts model q are discussed. It is found that some regularities exist and D_(con) D and Q are important parameters to characterise a fractal. It is also found that Suzuki's inequality, v(d)>v(d')for d<d', does not hold for d=min(D_(con)D_(con)).