Charbonneau Patrick, Yaida Sho
Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
Department of Physics, Duke University, Durham, North Carolina 27708, USA.
Phys Rev Lett. 2017 May 26;118(21):215701. doi: 10.1103/PhysRevLett.118.215701.
The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon-the Gardner transition-has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, d_{u}=6. Here, we obtain evidence for the existence of these transitions in d<d_{u} using a two-loop calculation. Because the critical fixed point is found in the strong-coupling regime, we corroborate the result by resumming the perturbative series with inputs from a three-loop calculation and an analysis of its large-order behavior. Our study offers a resolution of the long-lasting controversy surrounding phase transitions in finite-dimensional disordered systems.
自由能景观从平滑到分层的转变是平均场无序系统最丰富的特征之一。一个经过充分研究的例子是磁场中自旋玻璃的德阿尔梅达 - 图勒斯转变，并且最近有人预测结构玻璃会出现类似现象——加德纳转变。然而，在其临界维度上限(d_{u}=6)以下，这些破复本对称性相变的存在长期以来一直受到质疑。在这里，我们通过双圈计算获得了在(d < d_{u})时这些转变存在的证据。由于临界不动点是在强耦合区域找到的，我们通过用三圈计算的输入重新求和微扰级数并分析其高阶行为来证实这一结果。我们的研究解决了围绕有限维无序系统相变的长期争议。
