Abstract

The “temperature–defect concentration” phase diagram of quasi-one-dimensional Ising models with defects of the “random local field” type is studied. The competition of the tendency to the formation of a long-range order due to a weak interaction between one-dimensional spin chains and the tendency to the formation of the Imry–Ma phase in which the order parameter follows fluctuations of a random field induced by defects is studied too. The formation of the Imry–Ma phase is shown to be possible in the situation as the space dimension is higher than the lower critical dimension. The problem of the existence a long-range order in the Ising model with random fields is considered in a space with critical dimension d_i = 2.

中文翻译：

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带有“随机局部场”类型缺陷的准一维伊辛模型：维数大于下临界维数的空间中的伊曼-马相

摘要

研究了具有“局部局域”类型缺陷的准一维伊辛模型的“温度-缺陷浓度”相图。由于一维自旋链之间相互作用较弱而形成长程有序趋势的竞争，以及因阶跃参数跟随由激光诱导的随机场波动而形成的Imry-Ma相的趋势的竞争缺陷也在研究中。由于空间尺寸大于下临界尺寸，因此在这种情况下可能形成Imry-Ma相。在临界尺寸为d _i = 2的空间中，考虑具有随机场的Ising模型中存在一个长阶问题。