Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales
Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales
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多重 Schramm–Loewner 演化和统计力学鞅
DOI：
10.1007/s10955-005-7002-5
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发表时间：
2005
影响因子：
1.6
通讯作者：
Kalle Kytölä
中科院分区：
文献类型：
--
作者：
M. Bauer;D. Bernard;Kalle Kytölä
将配分函数与鞅相关的统计力学论证用于获得随机几何过程可以在临界点描述二维统计力学中的界面的条件。需要多个 SLE 来满足此条件会导致一些自然过程，我们将在本说明中研究这些过程。我们给出了此类多个 SLE 的示例，并讨论了共形块的选择如何与接口的几何配置相关，以及混合共形块的物理含义是什么。我们通过在渗滤和伊辛模型中的应用来说明具体计算的一般思想
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to satisfy this condition leads to some natural processes, which we study in this note. We give examples of such multiple SLEs and discuss how a choice of conformal block is related to geometric configuration of the interfaces and what is the physical meaning of mixed conformal blocks. We illustrate the general ideas on concrete computations, with applications to percolation and the Ising model