Nota de FísicaPublicado
Equation of States for the Infinite Cluster and Backbone in Anisotropic Square Lattice
L. R. Silva; N.S. Almeida; C. Tsallis
1985
Dados da publicação
- Autores
- L. R. Silva; N.S. Almeida; C. Tsallis
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 1985
- Descrição
- We use a real space renormalization group procedure recently, developed for calculating equations of states for geometrical problems, to treat bond percolation in the anisotropic square lattice. By choosing a convenient self-dual cluster, we calculate, ''for all values of the occupancy probabilities'' <math>p_x \,\!</math> and <math>p_y \,\!</math> (along the x and y axes respectively), the order parameters <math>P_\infty(p_x,p_y)\,\!</math> and <math>P_\infty^B(p_x,p_y)\,\!</math> respectively associated with the complete percolating infinite cluster and with its backbone. An interesting difference appears between these two quantities whenever one of the occupancy probabilities, say py , equals unity: <math>\lim_{p_y\rightarrow 1} P_\infty(p_x,p_y )\,\!</math> is ''discontinuous'' at <math>p_x\,\!</math> = 0 (where <math>P_\infty</math> jumps from 0 to 1), whereas <math>\lim_{p_y\rightarrow 1}P_\infty^B(p_x,p_y)\,\!</math> ''continuously increases'' from 0 to 1 when <math>p_x\,\!</math> increases from 0 to 1. Through a convenient extrapolation procedure which includes the use of the best available values for the critical exponents <math>\beta\,\!</math> and <math>\beta^B\,\!</math>, we obtain values for <math>P_\infty \,\!</math> and <math>P_\infty^B\,\!</math> which are believed to be numerically quite reliable. In particular <math>P_\infty (p,p) \sim \,\!</math> <math>A (p-1/2)^\beta (\beta =5/36 \,\!</math> and A=1.25) and <math> P_ \infty ^B(p,p)\sim A^B(p-1/2)^{\beta^{B}} ( ^{\beta^{B}}\simeq 0.53 </math> and <math> A^B \simeq 1.92 )</math> .
- Ano
- 1985
- Número
- CBPF-NF-024/85
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não