The calculation of multifractal properties of directed random walks on hierarchic trees with continuous branching

被引：2

作者：

Saakian, David B. ^{[1
,2
,3
]}

机构：

[1] Acad Sinica, Inst Phys, Taipei 11529, Taiwan

[2] Fdn Yerevan, Yerevan Phys Inst, AI Alikhanyan Natl Sci Lab, Yerevan 375036, Armenia

[3] Natl Taiwan Univ, Div Phys, Natl Ctr Theoret Sci N, Taipei 10617, Taiwan

来源：

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2012年

关键词：

scaling in socio-economic systems; disordered systems (theory); RANDOM-ENERGY MODEL; POLYMERS; EXPONENTS; LIMIT;

D O I：

10.1088/1742-5468/2012/04/P04007

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We consider the hierarchic tree random energy model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal distribution of random variables, as well as for the general case. We compare our results for the moments of the partition function with corresponding results of logarithmic 1d REM and conjecture a specific power law tail for the partition function distribution in the high-temperature phase. Our results establish a connection between reaction-diffusion equations and multi-scaling.

引用

页数：11

共 43 条

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