One-step replica-symmetry-breaking phase below the de Almeida–Thouless line in low-dimensional spin glasses
One-step replica-symmetry-breaking phase below the de Almeida–Thouless line in low-dimensional spin glasses
复制标题
低维自旋玻璃中德阿尔梅达-Thouless线下方的一步复制对称破缺相
DOI：
10.1103/physreve.101.042114
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发表时间：
2020
影响因子：
2.4
通讯作者：
Read, N.
中科院分区：
文献类型：
--
作者：
Höller, J.;Read, N.
根据平均场理论，de Almeida-Thouless （AT）线是Ising自旋玻璃温度-磁场平面上的相边界，在此位置发生从顺磁体到复制对称破缺（RSB）相的连续（即二阶）转变。本文利用一维空间中近程Ising自旋玻璃的brray - roberts约简landau - ginzburg型理论的场理论微扰重整化群方法，证明了非零磁场对相应跃迁性质的修正：(a)对于小且正的，随着AT线上场的增大，首先，跃迁下方的有序相变为所谓的一步RSB，而不是平均场理论中出现的全RSB；AT线上的转换保持连续，相关长度发散。然后，在更高的场中，一个三临界点将后一阶跃迁与准一阶跃迁分开，即相关长度不发散，部分阶参量有跳跃，但没有潜热。三临界点的位置趋于零。(b)因为，我们认为准一阶跃迁可以持续到任意小的非零场，在较低温度下仍然可以过渡到完全RSB。当准一阶跃迁发生时，它的温度高于同一场的at跃迁，随着温度的降低而抢先发生。这些结果可以解释在一些模拟和高温系列膨胀中，低维自旋玻璃在磁场存在下没有发散相关长度的报道。我们还注意到发生在准一阶跃迁温度以上的“动态冻结”状态与一步RSB相的“亚稳态”状态的相似性，并讨论了两者中纯态的数量问题。
The de Almeida–Thouless (AT) line is the phase boundary in the temperature–magnetic field plane of an Ising spin glass at which a continuous (i.e., second-order) transition from a paramagnet to a replica-symmetry-breaking (RSB) phase occurs, according to mean-field theory. Here, using field-theoretic perturbative renormalization group methods on the Bray-Roberts reduced Landau-Ginzburg-type theory for a short-range Ising spin glass in space of dimension, we show that atnonzeromagnetic field the nature of the corresponding transition is modified as follows: (a) Forsmall and positive, with increasing field on the AT line, first, the ordered phase just below the transition becomes the so-called one-step RSB, instead of the full RSB that occurs in mean-field theory; the transition on the AT line remains continuous with a diverging correlation length. Then at a higher field, a tricritical point separates the latter transition from a quasi-first-order one, that is one at which the correlation length does not diverge, and there is a jump in part of the order parameter, but no latent heat. The location of the tricritical point tends to zero as. (b) For, we argue that the quasi-first-order transition could persist down to arbitrarily small nonzero fields, with a transition to full RSB still expected at lower temperature. Whenever the quasi-first-order transition occurs, it is at a higher temperature than the AT transition would be for the same field, preempting it as the temperature is lowered. These results may explain the reported absence of a diverging correlation length in the presence of a magnetic field in low-dimensional spin glasses in some simulations and in high-temperature series expansions. We also draw attention to the similarity of the “dynamically frozen” state, which occurs at temperatures just above the quasi-first-order transition, and the “metastate-average state” of the one-step RSB phase, and discuss the issue of the number of pure states in either.