Theoretical Studies of Frustrated Systems

这笔赠款支持对相互作用中的受挫系统，即竞争系统进行理论和计算研究。这项工作将集中在一组便于研究的特殊系统上，即自旋玻璃。然而，这项研究的结果将具有广泛的适用性。由于系统陷入局部极小，自旋玻璃在低温下的动力学非常缓慢。实验上观察到了一系列令人惊讶的非平衡效应，但在伊辛系统(即具有离散自旋的系统)的模拟中很难看到这些效应。在以前的工作中已经强调了研究矢量自旋玻璃系统的必要性，事实上，在关于矢量自旋玻璃的实验中，非平衡效应比伊辛自旋玻璃更强烈。因此，将研究矢量自旋玻璃的非平衡和平衡行为，目的是详细解释实验结果。此外，还将研究比现有算法更有效的算法。对于有限温度模拟，目前最好的加速平衡的技术是并行回火，在这种技术中，系统的温度上下浮动，因此在高温下很容易克服障碍。我们将研究使用量子涨落是否会比使用热涨落更有效。已经有证据表明，用于寻找基态但不给出有限温度下的平衡行为的量子模拟“模拟退火法”比最初的热版本更有效。我们还将研究一种完全不同的算法，该算法基于状态密度的计算，原则上可以从该算法中获得关于任何温度的信息。在更长的时间范围内，我们将研究一个在组合优化问题中取得巨大成功的算法，但它植根于自旋玻璃的思想，是否可以用来更有效地寻找自旋玻璃基态。由于自旋玻璃的数值研究不可避免地被限制在相当小的尺寸，即使是最好的可用的算法，找到在增加尺寸时尽可能快地接近渐近临界行为的模型也是有用的。因此，我们将研究一族自旋玻璃模型，试图找到一个子空间，在这个子空间中，对有限尺寸标度的主要修正消失，这将使从较小的晶格尺寸获得可靠的结果。这些自旋玻璃的研究结果将对其他领域的研究具有广泛的适用性。此外，这项研究为学生提供了很好的培训。%这笔助学金支持对有挫折的系统的理论和计算研究，即在他们的互动中，竞争。这项工作将集中在一组便于研究的特殊系统上，即自旋玻璃。这些自旋玻璃的研究结果将对其他领域的研究具有广泛的适用性。此外，本研究还为学生提供了良好的培训。*

This grant supports theoretical and computational research on systems with frustration, i.e., competition, in their interactions. The work will focus on a particular set of systems that is convenient to study, the spin glass. However, the results of this research will have wide applicability.The dynamics of spin glasses at low temperatures is very slow because the system gets trapped in local minima. A range of surprising non-equilibrium effects have been observed experimentally, but these have been hard to see in simulations on Ising systems, i.e., systems with discrete spins. In previous work the need to investigate vector spin glass systems has been emphasized, and indeed the non-equilibrium effects are seen more strongly in experiments on vector spin glasses than Ising spin glasses. Thus, non-equilibrium and equilibrium behavior of vector spin glasses will be studied with the intent of explaining experimental results in detail.Also, studies will be made to find algorithms that are more efficient than those currently available. For finite-temperature simulations, the best current techniques for speeding up equilibration is parallel tempering, in which the temperature of the system wanders up and down, so it can easily overcome barriers when at high temperature. We will investigate if using quantum, rather than thermal, fluctuations will be more efficient. Already there is evidence that the quantum analogue of "simulated annealing," which is used to find the ground states but does not give equilibrium behavior at finite temperature, is more efficient than the original thermal version. We will also investigate a quite different algorithm, based on a calculation of the density of states, from which one can, in principle, get information about any temperature. On a longer time frame, we will investigate whether an algorithm used with great success for a problem in combinatorial optimization, but rooted in ideas from spin glasses, can be used to find spin glass ground states more efficiently.Since numerical studies of spin glasses are inevitably restricted to rather small sizes, even with the best available algorithms, it is useful to find models which approach the asymptotic critical behavior as fast as possible on increasing the size. Thus, we will study a family of spin glass models to try to find a subspace in which the leading correction to finite-size scaling vanishes, which would enable reliable results to be obtained from smaller lattice sizes. The results of these studies on spin glasses will have wide applicability to other fields of study. In addition, this research provides excellent training for students.%%% This grant supports theoretical and computational research on systems with frustration, i.e., competition, in their interactions. The work will focus on a particular set of systems that is convenient to study, the spin glass. The results of these studies on spin glasses will have wide applicability to other fields of study. In addition, this research provides excellent training for students.***