Mendeley出力
＜研究報告書＞
Abelian Sandpile Models in Statistical Mechanics : Dissipative Abelian Sandpile Models
| 作成者 | |
|---|---|
| 本文言語 | |
| 出版者 | |
| 発行日 | |
| 収録物名 | |
| 巻 | |
| 開始ページ | |
| 終了ページ | |
| 出版タイプ | |
| アクセス権 | |
| 関連DOI | |
| 関連URI | |
| 関連情報 | |
| 概要 | We introduce a family of abelian sandpile models with two parameters n, m ∈ N defined on finite lattices on d-dimensional torus. Sites with 2dn + m or more grains of sand are unstable and topple, and ...in each toppling m grains dissipate from the system. Because of dissipation in bulk, the models are well-defined on the shift-invariant lattices and the infinite-volume limit of systems can be taken. From the determinantal expressions, we obtain the asymptotic forms of the avalanche propagators and the height-(0, 0) correlations of sandpiles for large distances in the infinite-volume limit in any dimensions d ≥ 2. We show that both of them decay exponentially with the correlation length ξ(d, a) = (√<d> sinh^<−1>√<a(a + 2)> )^<−1>, if the dissipation rate a = m/(2dn) is positive. Considering a series of models with increasing n, we discuss the limit a ↓ 0 and the critical exponent defined by ν_a = −< lim>___<a↓0> (log ξ(d, a)) (log a) is determined as ν_a = 1 2 for all d ≥ 2. Comparison with the q ↓ 0 limit of q-state Potts model in external magnetic field is discussed.続きを見る |
| 目次 | 1.Introduction 2.Basic Properties of Dissipative Abelian Sandpile Model 3.Avalanche Propagators 4.Height-0 Density and Height-(0, 0) Correlations 5.Discussions |
詳細
| PISSN | |
|---|---|
| NCID | |
| レコードID | |
| 査読有無 | |
| 主題 | |
| ISSN | |
| 登録日 | 2015.09.25 |
| 更新日 | 2023.10.05 |