The Models of Ising and Heisenberg
The Models of Ising and Heisenberg
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伊辛和海森堡的模型
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
H. Stöcker
中科院分区：
文献类型：
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作者：
W. Greiner;L. Neise;H. Stöcker
相变的理论描述是非常困难的。我们已经在前面的章节中解释了其中的一些原因。只有少数模型可以在统计力学的框架内处理，而无需大量的数值工作。一个是由于伦茨（1920年），后来详细制定了他的学生伊辛（1925年）。最初，它是为居里温度下铁磁体的相变而发明的;然而，随着时间的推移，人们意识到，只需稍加改变，该模型也可以应用于其他相变，如二元合金中的有序-无序相变。此外，该模型可以应用于多粒子物理学的几个现代问题，例如用于描述所谓的自旋玻璃。这些金属具有非晶态结构而不是晶态结构，它们具有在T = 0时熵不为零的有趣性质。最近，人们意识到伊辛的想法（以修改后的形式）也可以解释模式识别的示意性神经网络。因此，该模型对于人脑模型的开发越来越重要。
The theoretical description of phase transitions is very difficult. We have already explained some reasons for this in the preceding sections. Only a few models can be treated in the framework of statistical mechanics without large numerical efforts. One is due to Lenz (1920), and was later on worked out in detail by his pupil Ising (1925). Originally, it was invented for the phase transition of ferromagnets at the Curie temperature; however, in the course of time it was realized that with only slight changes the model can also be applied to other phase transitions, like order-disorder transitions in binary alloys. Furthermore, the model may be applied to several modern problems of many-particle physics, for instance for the description of so-called spin glasses. These are metals having amorphous instead of crystalline structures, which have the interesting property of nonvanishing entropy at T = O. Recently, it has been realized that Ising’s idea (in modified form) could also explain pattern recognition in schematic neural networks. Thus, this model gains more and more importance for the development of models for the human brain.