We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify, and explain, two distinct regimes, separated by a critical density $n_c$. Below $n_c$, the per-particle exchange energy is lowered by the contribution of L=1, whereas above $n_c$ it is increased. As special cases of our general equation we recover various known, more limited, results for higher fields, and identify and correct a few inconsistencies in some of these earlier expressions.
Replica-exchange Wang-Landau sampling: Pushing the limits of Monte Carlo simulations in materials sciences
我们描述了使用复制交换Wang-Landau（REWL）采样的材料的热力学研究，这是一种用于大规模并行实现Wang-Landau Monte Carlo方法的通用框架。为了评估该方法的性能和可扩展性，我们使用经典的海森堡模型参数化的第一性原理计算研究体心立方（bcc）铁的磁相变。我们证明，我们的框架导致了显着的加速，而不影响的准确性和精度，并有利于研究更大的系统比它的串行对应。
Landau theory and exchange instabilities in Mn$_5$Si$_3$: A case against strain-induced altermagnetism
Department of Physics and Astronomy and Nebraska Center for Materials and Nanoscience, University of Nebraska–Lincoln（内布拉斯加大学林肯分校物理与天文学系及内布拉斯加材料与纳米科学中心）
Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence
Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction
本文给出了均匀电子气与库仑作用的长程部分相互作用的静态交换关联核在实空间和倒易空间中的一个简单近似表达式。该表达式在小和大波矢量处的该内核的精确渐近行为之间插值，这反过来又需要来自具有在G 0 W 0近似中计算的相同相互作用的均匀电子气的动量分布的信息。这种交换相关内核以及它的补充类似物相关的短程部分的库仑相互作用比库仑交换相关内核更本地化，并构成潜在的成分，在最近的绝热连接波动耗散和/或密度泛函理论的方法的电子相关问题的基础上，一个单独的治疗远程和短程相互作用的影响的近似。
