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Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: Above and below the upper critical range
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-07 , DOI: 10.1103/physreve.104.034105
S Jensen 1 , N Read 2, 3 , A P Young 4
Affiliation  

Understanding the low-temperature pure state structure of spin glasses remains an open problem in the field of statistical mechanics of disordered systems. Here we study Monte Carlo dynamics, performing simulations of the growth of correlations following a quench from infinite temperature to a temperature well below the spin-glass transition temperature Tc for a one-dimensional Ising spin-glass model with diluted long-range interactions. In this model, the probability Pij that an edge {i,j} has nonvanishing interaction falls as a power law with chord distance, Pij∝1/Rij2σ, and we study a range of values of σ with 1/2<σ<1. We consider a correlation function C4(r,t). A dynamic correlation length that shows power-law growth with time ξ(t)∝t1/z can be identified in the data and, for large time t, C4(r,t) decays as a power law r−αd with distance r when r≪ξ(t). The calculation can be interpreted in terms of the maturation metastate averaged Gibbs state, or MMAS, and the decay exponent αd differentiates between a trivial MMAS (αd=0), as expected in the droplet picture of spin glasses, and a nontrivial MMAS (αd≠0), as in the replica-symmetry-breaking (RSB) or chaotic pairs pictures. We find nonzero αd even in the regime σ>2/3 which corresponds to short-range systems below six dimensions. For σ<2/3, the decay exponent αd follows the RSB prediction for the decay exponent αs=3−4σ of the static metastate, consistent with a conjectured statics-dynamics relation, while it approaches αd=1−σ in the regime 2/3<σ<1; however, it deviates from both lines in the vicinity of σ=2/3.

中文翻译：
一维长程伊辛自旋玻璃中的非平凡成熟转移平均状态：高于和低于上限临界范围

了解自旋玻璃的低温纯态结构仍然是无序系统统计力学领域的一个悬而未决的问题。在这里，我们研究蒙特卡罗动力学，模拟从无限温度淬火到远低于自旋玻璃化转变温度的温度后相关性的增长吨C对于具有稀释的长程相互作用的一维 Ising 自旋玻璃模型。在这个模型中，概率磷一世j 那个边缘 {一世,j} 有非零相互作用下降为具有弦距的幂律， 磷一世j∝1/电阻一世j2σ，我们研究了一系列的值 σ 和 1/2<σ<1. 我们考虑一个相关函数C4(r,吨). 显示幂律随时间增长的动态相关长度ξ(吨)∝吨1/z 可以在数据中识别，并且在很长一段时间内 吨, C4(r,吨) 作为幂律衰减 r-αd 有距离 r 什么时候 r≪ξ(吨). 该计算可以解释为成熟转移平均吉布斯状态或 MMAS，以及衰减指数αd 区分微不足道的 MMAS (αd=0)，正如在旋转眼镜的液滴图片中所预期的那样，以及一个非平凡的 MMAS (αd≠0)，如在副本对称性破坏 (RSB) 或混沌对图片中。我们发现非零αd 即使在政权σ>2/3这对应于六维以下的短程系统。为了σ<2/3，衰减指数 αd 遵循衰减指数的 RSB 预测 α秒=3-4σ的的静态亚状态，有推测静动力学关系一致，但它接近αd=1-σ 在政权 2/3<σ<1; 然而，它偏离了附近的两条线σ=2/3.
更新日期：2021-09-07
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