用多能级模型描述固体中的Specific Heat反常
Specific Heat Anomalies in Solids Described by a Multilevel Model
摘要：
比热测量是探测固体基本激发的最有力的实验方法之一。在一个多世纪前爱因斯坦模型提出之后（Annalen der Physik \textbf{22}，180（1907）），已经提出了几个理论模型来描述实验结果。在这里，我们报告中观察到的几种材料的双峰比热异常的详细分析。采用一个简单的多层次模型，改变能级之间的间距$Δ_i$ = $(E_i$ $-$ $E_{0})$和每个能级的简并度$g_i$，我们得出出现这种异常所需的条件。我们的研究结果表明，$Δ_2$ / $Δ_1$ $\thickapprox$ 10之间的能量水平和高简并的一个能级定义的双峰制度的比热。我们的方法准确地匹配最近的实验结果。此外，使用平均场的方法，我们计算了一个退化的肖特基类系统进行铁磁（FM）相变的比热。结果表明，随着简并度的增加，比热的肖特基最大值变窄，而与FM转变相关的峰不受影响。
英文摘要：
Specific heat measurements constitute one of the most powerful experimental methods to probe fundamental excitations in solids. After the proposition of Einstein's model, more than one century ago (Annalen der Physik \textbf{22}, 180 (1907)), several theoretical models have been proposed to describe experimental results. Here we report on a detailed analysis of the two-peak specific heat anomalies observed in several materials. Employing a simple multilevel model, varying the spacing between the energy levels $Δ_i$ = $(E_i$ $-$ $E_{0})$ and the degeneracy of each energy level $g_i$, we derive the required conditions for the appearance of such anomalies. Our findings indicate that a ratio of $Δ_2$/$Δ_1$ $\thickapprox$ 10 between the energy levels and a high degeneracy of one of the energy levels define the two-peaks regime in the specific heat. Our approach accurately matches recent experimental results. Furthermore, using a mean-field approach we calculate the specific heat of a degenerate Schottky-like system undergoing a ferromagnetic (FM) phase transition. Our results reveal that as the degeneracy is increased the Schottky maximum in the specific heat becomes narrow while the peak associated with the FM transition remains unaffected.
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