Theoretical Studies of Frustrated Systems

该基金支持理论和计算研究系统与挫折，即竞争，在他们的相互作用。这项工作将集中在一组便于研究的系统上，即自旋玻璃。然而，本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非常缓慢，因为系统被困在局部极小值中。一系列令人惊讶的非平衡效应已经在实验中观察到，但这些在模拟伊辛系统（即具有离散自旋的系统）中很难看到。在以前的工作中，研究矢量自旋玻璃系统的必要性已经得到了强调，事实上，在矢量自旋玻璃的实验中，非平衡效应比伊辛自旋玻璃更明显。因此，我们将研究矢量自旋玻璃的非平衡和平衡行为，并详细解释实验结果。此外，还将进行研究，寻找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平行回火，在这种技术中，系统的温度上下波动，因此在高温下它可以很容易地克服障碍。我们将研究使用量子波动而不是热波动是否会更有效。已经有证据表明，“模拟退火”的量子模拟，用于寻找基态，但不给出有限温度下的平衡行为，比原始的热版本更有效。我们还将研究一种完全不同的算法，它基于状态密度的计算，原则上，人们可以从中得到任何温度的信息。在更长的时间框架内，我们将研究一种基于自旋玻璃的思想，在组合优化问题上取得巨大成功的算法，是否可以更有效地用于寻找自旋玻璃基态。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，即使使用最好的可用算法，找到在尺寸增加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，在该子空间中，对有限尺寸尺度的主要校正消失，这将使从较小的晶格尺寸获得可靠的结果成为可能。这些关于自旋玻璃的研究结果将对其他研究领域具有广泛的适用性。此外，本研究为学生提供了良好的训练。该基金支持在相互作用中存在挫折（即竞争）的系统的理论和计算研究。这项工作将集中在一组便于研究的系统上，即自旋玻璃。这些关于自旋玻璃的研究结果将对其他研究领域具有广泛的适用性。此外，本研究为学生提供了良好的训练

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.***