We explore order in low angle grain boundaries (LAGBs) embedded in a two-dimensional crystal at thermal equilibrium. Symmetric LAGBs subject to a Peierls potential undergo, with increasing temperatures, a thermal depinning transition; above which, the LAGB exhibits transverse fluctuations that grow logarithmically with interdislocation distance. Longitudinal fluctuations lead to a series of melting transitions marked by the sequential disappearance of diverging algebraic Bragg peaks with universal critical exponents. Aspects of our theory are checked by a mapping onto random matrix theory.

中文翻译：

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二维低角度晶粒边界的统计力学

我们探索在热平衡时嵌入二维晶体的低角度晶界（LAGB）的顺序。具有Peierls势的对称LAGB随温度的升高而发生热脱钉转变；在此之上，LAGB表现出横向波动，该波动随位错距离成对数增长。纵向波动导致一系列熔化转变，其特征是具有通用临界指数的发散的布拉格峰的相继消失。通过映射到随机矩阵理论来检验我们理论的各个方面。