An analytical expression for the energy of indirect exchange interaction of two magnetic impurities in a one-dimensional crystal has been obtained taking into account both disorder and temperature. The inclusion of even a weak disorder in a one-dimensional crystal leads to the localization of charge carriers in it and, as a result, to the suppression of the long-range indirect exchange interaction (RKKY interaction) between two magnetic impurities at the localization length of charge carriers. An increase in the temperature, in turn, causes the disappearance of electron density coherence, which provides the RKKY interaction. It has been shown that these two effects are independent of each other and exponentially suppress the exchange interaction with an increase in the distance between the impurities. Another important manifestation of disorder is a change in the power dependence on the distance between the impurities: the RKKY interaction decreases with distance faster than 1/r.

中文翻译：

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考虑到无序和温度，一维晶体中的RKKY相互作用

考虑到无序和温度，已经获得了一维晶体中两种磁性杂质间接交换相互作用的能量的解析表达式。一维晶体中甚至包含一个弱无序，都会导致载流子在其中定位，结果，抑制了两个磁性杂质之间的长期间接交换相互作用（RKKY相互作用）电荷载体的长度。温度升高又导致电子密度相干性消失，从而提供了RKKY相互作用。已经表明，这两种作用是彼此独立的，并且随着杂质之间距离的增加而指数地抑制交换相互作用。[R 。