Yeo J, Moore M A
Department of Physics, Konkuk University, Seoul 05029, Korea.
Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
Phys Rev E. 2020 Mar;101(3-1):032127. doi: 10.1103/PhysRevE.101.032127.
The fully connected Ising p-spin model has for p>2 a discontinuous phase transition from the paramagnetic phase to a stable state with one-step replica symmetry breaking (1RSB). However, simulations in three dimension do not look like these mean-field results and have features more like those which would arise with full replica symmetry breaking (FRSB). To help understand how this might come about we have studied in the fully connected p-spin model the state of two-step replica symmetry breaking (2RSB). It has a free energy degenerate with that of 1RSB, but the weight of the additional peak in P(q) vanishes. We expect that the state with full replica symmetry breaking (FRSB) is also degenerate with that of 1RSB. We suggest that finite-size effects will give a nonvanishing weight to the FRSB features, as also will fluctuations about the mean-field solution. Our conclusion is that outside the fully connected model in the thermodynamic limit, FRSB is to be expected rather than 1RSB.
对于(p>2)的全连接伊辛(p)自旋模型，存在从顺磁相到具有一步复制对称破缺（1RSB）的稳定态的不连续相变。然而，三维模拟结果与这些平均场结果不同，其特征更类似于完全复制对称破缺（FRSB）所产生的特征。为了帮助理解这种情况是如何发生的，我们在全连接(p)自旋模型中研究了两步复制对称破缺（2RSB）的状态。它具有与1RSB简并的自由能，但(P(q))中额外峰值的权重消失。我们预计完全复制对称破缺（FRSB）的状态也与1RSB简并。我们认为，有限尺寸效应将使FRSB特征具有非零权重，平均场解附近的涨落也会如此。我们的结论是，在热力学极限下，除了全连接模型之外，预计会出现FRSB而不是1RSB。
