[论文解读] Overfrustrated and Underfrustrated Spin-Glasses in d=3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2

Efe İlker, A. Nihat Berker|arXiv (Cornell University)|Dec 1, 2013

Theoretical and Computational Physics被引用 3

一句话总结

本文研究了通过局部相关冻结随机性连续调节阻挫——在d=3和d=2的层级格点上的伊辛体系中——对自旋玻璃相图的影响。研究发现，当51%的阻挫被消除时（f=0.49），d=2中出现自旋玻璃序；而当额外增加33%的阻挫时（g=0.67），d=3中自旋玻璃序消失，且混沌程度随阻挫增加而单调上升，其度量为李雅普诺夫指数。

ABSTRACT

In spin-glass systems, frustration can be adjusted continuously and considerably, without changing the antiferromagnetic bond probability p, by using locally correlated quenched randomness, as we demonstrate here on hypercubic lattices and hierarchical lattices. Such overfrustrated and underfrustrated Ising systems on hierarchical lattices in d=3 and 2 are studied. With the removal of just 51% of frustration, a spin-glass phase occurs in d=2. With the addition of just 33% frustration, the spin-glass phase disappears in d=3. Sequences of 18 different phase diagrams for different levels of frustration are calculated in both dimensions. In general, frustration lowers the spin-glass ordering temperature. At low temperatures, increased frustration favors the spin-glass phase (before it disappears) over the ferromagnetic phase and symmetrically the antiferromagnetic phase. When any amount, including infinitesimal, frustration is introduced, the chaotic rescaling of local interactions occurs in the spin-glass phase. Chaos increases with increasing frustration, as can be seen from the increased positive value of the calculated Lyapunov exponent λ, starting from λ=0 when frustration is absent. The calculated runaway exponent yR of the renormalization-group flows decreases with increasing frustration to yR=0 when the spin-glass phase disappears. From our calculations of entropy and specific-heat curves in d=3, it is shown that frustration lowers in temperature the onset of both long- and short-range order in spin-glass phases, but is more effective on the former. From calculations of the entropy as a function of antiferromagnetic bond concentration p, it is shown that the ground-state and low-temperature entropy already mostly sets in within the ferromagnetic and antiferromagnetic phases, before the spin-glass phase is reached.

研究动机与目标

• 探索如何在不改变自旋玻璃体系中反铁磁键概率p的前提下，连续调节阻挫。
• 研究在不同阻挫水平下，包括过度阻挫和欠阻挫区域，d=3和d=2体系相图的演化。
• 确定自旋玻璃长程序在低维体系中出现或消失的条件。
• 分析阻挫在诱导自旋玻璃相中相互作用的混沌重标度中的作用及其与李雅普诺夫指数的依赖关系。
• 考察阻挫对熵、比热以及长程和短程序起始的影响。

提出的方法

• 对d=3和d=2的层级格点应用精确的重整化群分析。
• 通过实现局部相关的冻结随机性，在保持p不变的同时调节阻挫水平。
• 在两个维度中，计算了18组不同阻挫水平下的完整相图。
• 计算李雅普诺夫指数λ，以量化自旋玻璃相中的混沌重标度。
• 评估重整化群流的发散指数y_R随阻挫的变化关系。
• 分析熵S和比热C随温度和反铁磁键浓度p的变化关系。

实验结果

研究问题

• RQ1 自旋玻璃体系中的阻挫能否在不改变反铁磁键浓度p的情况下实现连续调节？
• RQ2 在d=3和d=2中，自旋玻璃相消失的临界阻挫水平是多少？
• RQ3 增加阻挫如何影响自旋玻璃相中长程和短程序的起始温度？
• RQ4 即使存在微小阻挫，自旋玻璃相中是否会发生相互作用的混沌重标度？其与阻挫的标度关系如何？
• RQ5 阻挫在达到自旋玻璃相之前，对铁磁和反铁磁相的基态和低温熵在多大程度上产生预置影响？

主要发现

• 当51%的阻挫被消除时（f=0.49），d=2中出现自旋玻璃相，表明在欠阻挫条件下，二维体系中自旋玻璃序可以存在。
• 在d=3中，当额外增加33%的阻挫时（g=0.67），自旋玻璃相消失，表明过度阻挫会抑制自旋玻璃序。
• 李雅普诺夫指数λ随阻挫增加而上升，从无阻挫时的λ=0开始，进入自旋玻璃相后变为正值，证实了混沌的出现。
• 随着阻挫增加，重整化群流的发散指数y_R从d−1下降至0，当自旋玻璃相消失时恰好归零。
• 阻挫对长程序起始温度的影响比对短程序更显著，熵和比热曲线根据阻挫水平表现出明显不同的区域。
• 在达到自旋玻璃相之前，基态和低温熵主要在铁磁和反铁磁相中已基本确立，表明阻挫在自旋玻璃序出现前主导了熵的贡献。