| Автор | P J Reynolds |
| Автор | H E Stanley |
| Автор | W Klein |
| Дата выпуска | 1977-11-01 |
| dc.description | The percolation problem is solved exactly in one dimension. The functions obtained bear a strong resemblance to those of the n-vector model on the same lattice. Further, a ghost field is included exactly in all dimensions d, thereby treating the 'thermodynamics' of percolation without appealing to the Potts model. In particular, it is shown that for d=1 that the nature of the singularities near the critical percolation probability, p<sub>c</sub>=1, is described by alpha <sub>p</sub>= gamma <sub>p</sub>=1, beta <sub>p</sub>=0, and delta <sub>p</sub>= infinity . The pair connectedness and correlation length are calculated explicitly, and eta <sub>p</sub>= nu <sub>p</sub>=1, in agreement with the hyperscaling relation d nu <sub>p</sub>=2- alpha <sub>p</sub>. Finally, scaling is demonstrated for both the cluster size distribution and the percolation function analogous to the Gibbs free energy, and the scaling powers are explicitly evaluated; in particular, the exponents sigma =1 and tau =2, are found. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Ghost fields, pair connectedness, and scaling: exact results in one-dimensional percolation |
| Тип | lett |
| DOI | 10.1088/0305-4470/10/11/007 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 10 |
| Первая страница | L203 |
| Последняя страница | L209 |
| Аффилиация | P J Reynolds; Dept. of Phys., Boston Univ., Boston, MA, USA |
| Аффилиация | H E Stanley; Dept. of Phys., Boston Univ., Boston, MA, USA |
| Аффилиация | W Klein; Dept. of Phys., Boston Univ., Boston, MA, USA |
| Выпуск | 11 |
