On the lowering of dimensionality in phase transitions with random fields
On the lowering of dimensionality in phase transitions with random fields
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关于随机场相变的降维
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
A. Young
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文献类型：
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作者：
A. Young
作者重新阐述了 Aharony、Imry 和 Ma 的证明（Phys. Rev. Lett., vol.37, p.1364 (1976)），即对于微扰理论中的所有阶，具有短程相互作用和淬灭随机场的 d 维系统的临界指数与 (d-2) 维纯系统的临界指数相同。因此，作者明确地证明了这些系统之间对于具有多个动量积分的项的等价性，其中涉及不平凡的组合因素。如果力是长范围的，随着距离 R 变化，如 R-(d+ sigma )，则 d 维随机系统与 (d- sigma ) 维度中相应的纯系统之间所提出的等价性通常不成立，并且通过 (=3-d) 中的二阶计算明确证明了这一点。
The author reformulates the proof by Aharony, Imry and Ma (Phys. Rev. Lett., vol.37, p.1364 (1976)) that, to all orders in perturbation theory, the critical exponents of a d-dimensional system with short-range interaction and a quenched random field are the same as those of a (d-2) dimensional pure system. The author thus shows explicitly the equivalence between these systems for terms with several momentum integrations, which involve non trivial combinatorial factors. If the forces are of long range, varying with distance R like R-(d+ sigma ), the proposed equivalence between a d-dimensional random system and the corresponding pure system in (d- sigma ) dimensions is shown not to hold in general and this is demonstrated explicitly by a calculation to second order in in (=3-d).