Theoretical Studies of Frustrated Systems

该补助金支持对挫折系统的理论和计算研究，即，竞争，在互动中。 这项工作将集中在一组便于研究的特定系统上，即自旋玻璃。 然而，这项研究的结果将具有广泛的适用性。自旋玻璃在低温下的动力学是非常缓慢的，因为系统被困在局部极小值。 实验上已经观察到一系列令人惊讶的非平衡效应，但这些在伊辛系统的模拟中很难看到，即，具有离散自旋的系统 在以前的工作中，需要调查矢量自旋玻璃系统已被强调，事实上，非平衡效应被视为更强烈的矢量自旋玻璃比伊辛自旋玻璃的实验。 因此，为了对实验结果进行详细的解释，将对矢量自旋玻璃的非平衡态和平衡态行为进行研究，并研究比现有算法更有效的算法。 对于有限温度模拟，目前加速平衡的最佳技术是并行回火，其中系统的温度上下波动，因此在高温下可以轻松克服障碍。 我们将研究使用量子而不是热涨落是否会更有效。 已经有证据表明，量子模拟的“模拟退火”，这是用来找到基态，但不给在有限温度下的平衡行为，是更有效的比原来的热版本。 我们还将研究一种完全不同的算法，该算法基于态密度的计算，原则上，人们可以从中获得关于任何温度的信息。 在更长的时间框架内，我们将研究一种在组合优化问题中获得巨大成功的算法，但植根于自旋玻璃的思想，是否可以用来更有效地找到自旋玻璃基态。由于自旋玻璃的数值研究不可避免地局限于相当小的尺寸，即使使用最好的算法，找到在增加尺寸时尽可能快地接近渐近临界行为的模型是有用的。 因此，我们将研究一系列自旋玻璃模型，试图找到一个子空间，其中有限尺寸标度的主要校正消失，这将使可靠的结果从较小的晶格尺寸获得。 自旋玻璃的这些研究结果将对其他研究领域具有广泛的适用性。 此外，这项研究为学生提供了极好的培训。% 该补助金支持对挫折系统的理论和计算研究，即，竞争，在互动中。 这项工作将集中在一组便于研究的特定系统上，即自旋玻璃。 自旋玻璃的这些研究结果将对其他研究领域具有广泛的适用性。 此外，这项研究为学生提供了很好的培训。*

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.***