抄録
We study a statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We first show the existence of the thermodynamic limit of the (appropriately scaled) free energy. Then we show that there are two domains in the weight parameters (i.e. two phases) between which the scaling differs; i.e. there is a certain kind of phase transition in our model, and we find the critical exponents of the free energy at the phase transition point. We also show the convergence of the distribution of the scaled length of the paths at thermodynamic limit.
| 本文言語 | English |
|---|---|
| ページ（範囲） | 1-26 |
| ページ数 | 26 |
| ジャーナル | Probability Theory and Related Fields |
| 巻 | 84 |
| 号 | 1 |
| DOI | |
| 出版ステータス | Published - 1990 3 |
| 外部発表 | はい |
ASJC Scopus subject areas
- 分析
- 統計学および確率
- 統計学、確率および不確実性