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 $P\left(q\right)$ 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.

中文翻译：

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均值理论之外的一步复制对称性破坏inp自旋Ising模型的可能不稳定性

完全连接的伊辛 $p$自旋模型具有 $p>2$从顺磁相到稳定状态的不连续相变，一步复制对称性（1RSB）。但是，三维模拟看起来不像这些均值场结果，其特征更像是完全复制对称破坏（FRSB）所产生的特征。为了帮助理解这是怎么发生的，我们在完全连接的环境中进行了研究$p$-spin模型的两步副本对称破坏状态（2RSB）。它的自由能退化为1RSB，但是附加峰的权重为$P（q）$消失。我们预期具有完全复制对称性破坏（FRSB）的状态也会随着1RSB的状态而退化。我们建议，有限大小的影响将使FRSB特征的权重消失，平均场解的波动也将消失。我们的结论是，在热力学极限的完全连接模型之外，可以预期使用FRSB而不是1RSB。