Dimensional crossover in dilute magnets
Dimensional crossover in dilute magnets
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稀磁体中的维度交叉
DOI：
10.1088/0022-3719/13/30/020
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发表时间：
1980
期刊：
影响因子：
--
通讯作者：
R. B. Stinchcombe
中科院分区：
文献类型：
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作者：
R. B. Stinchcombe
讨论了稀释“低维”磁体（层状磁体和链状磁体）的临界曲线（转变温度Tc与浓度）。针对Ising情况，建立了一个基于实空间重整群计算和某些精确考虑的模型，并进行了分析。给出了不同类型层状和链状铁磁体和反铁磁体的不同交换比的临界曲线。对于伊辛层磁体，随着磁性浓度向二维渗透浓度降低，KTc下降，直到与层间的弱交换相当。这种弱交换将有效维数提高到3，从而使临界曲线变平，并朝着三维系统较小的极限浓度前进。对于准一维（链）Ising磁体，由于链间耦合，KTc仅是非零的。稀释导致KTc迅速下降到一个较小的值，这个值大致等于链间与链内耦合的比率，并最终在耦合链对应的更高维度的渗透浓度下消失。
A discussion is given of the critical curves (transition temperature Tc versus concentration) of diluted 'low dimensional' magnets (layer magnets, and chain magnets). A model based on real-space renormalisation-group calculations and certain exact considerations is constructed for the Ising case, and analysed. Resulting critical curves are given for various exchange ratios for various types of layer and chain ferro- and antiferromagnet. For the case of an Ising layer magnet, as the magnetic concentration is reduced towards the two-dimensional percolation concentration, KTc falls until it becomes comparable with the weak exchange between layers. This weak exchange raises the effective dimensionality to three so that the critical curve flattens off and heads towards the smaller limiting concentration for the three-dimensional system. For a quasi-one-dimensional (chain) Ising magnet, KTc is only non-zero by virtue of the interchain coupling. Dilution causes KTc to fall very rapidly to values smaller by a factor roughly equal to the ratio of interchain to intrachain couplings, and eventually to vanish at the percolation concentration for the higher dimensionality corresponding to coupled chains.