Dimensional Reduction for Generalized Continuum Polymers
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- 作者：Tyler Helmuth
- 关键词：Branched polymers ; Hard spheres ; Dimensional reduction ; Central hyperplane arrangements ; Combinatorial reciprocity ; Mayer expansion
- 刊名：Journal of Statistical Physics
- 出版年：2016
- 出版时间：October 2016
- 年：2016
- 卷：165
- 期：1
- 页码：24-43
- 全文大小：618 KB
- 刊物类别：Physics and Astronomy
- 刊物主题：Physics
Statistical Physics
Mathematical and Computational Physics
Physical Chemistry
Quantum Physics - 出版者：Springer Netherlands
- ISSN：1572-9613
- 卷排序：165
文摘
The Brydges–Imbrie dimensional reduction formula relates the pressure of a d-dimensional gas of hard spheres to a model of \((d+2)\)-dimensional branched polymers. Brydges and Imbrie’s proof was non-constructive and relied on a supersymmetric localization lemma. The main result of this article is a constructive proof of a more general dimensional reduction formula that contains the Brydges–Imbrie formula as a special case. Central to the proof are invariance lemmas, which were first introduced by Kenyon and Winkler for branched polymers. The new dimensional reduction formulas rely on invariance lemmas for central hyperplane arrangements that are due to Mészáros and Postnikov. Several applications are presented, notably dimensional reduction formulas for (i) non-spherical bodies and (ii) for corrections to the pressure due to symmetry effects.