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摘要翻译：
我们研究了具有单空位的正方形晶格上的经典二聚体模型，通过发展所有构型集合的图论分类，扩展了密排二聚体的生成树公式。利用这种形式，我们可以解决由二聚体滑动引起的空位的可能运动问题。在无限大系统中，我们发现空位被严格堵塞的概率为57/4-10sqrt[2]。更一般地说，空位可及的畴的尺寸分布以幂律衰减为特征，指数为9/8。在有限系统中，空位到达边界的概率随系统尺寸的幂律下降，指数为1/4。空位的弱局部化仍然允许无界扩散，其特征是扩散指数，我们将其与生成树上的扩散指数联系起来。我们还对该模型进行了自由边界条件和周期边界条件的数值模拟。
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英文标题：
《Vacancy localization in the square dimer model》
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作者：
J. Bouttier, M. Bowick, E. Guitter and M. Jeng
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. On a finite system, the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1/4. The resultant weak localization of vacancies still allows for unbounded diffusion, characterized by a diffusion exponent that we relate to that of diffusion on spanning trees. We also implement numerical simulations of the model with both free and periodic boundary conditions.
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PDF链接：
https://arxiv.org/pdf/706.1016
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