Fractal空间上自迴避行走的吸收问题

本文运用严格重整化群理论研究了两种Fractal空间上自迴避行走的吸收问题。计算所得的交跨指数φ和相关长度指数ν的严格解结果表明,de Gennes的推测公式φ=1—ν并不成立。相变流图与欧几里德空间中相应问题的流图定性相同。唯一而重要的差别在于Fractal空间中的吸收相变在无穷小吸收作用的硬壁影响下就可发生,而在欧几里德空间只是在一定大小的吸收作用下才会发生。 关键词：

ADSORPTION OF A SELF-AVOIDING WALK ON FRACTAL SPACES

An exact real space renormalisation group is applied to study the adsorption of a single self-avoiding walk on fractal spaces. Exact results of critical exponent ν and crossover exponent φ show that de Gennes' conjecture φ =1-ν is invalid. The phase diagram has qualitatively the same shape as it has on Euclidean space, except for a unique and important difference that the adsorption transition would take place for a single polymer chain at a hard wail exerting a infinitesimal short-range attractive force on the fractal space instead of a finite one as on Euclidean space.