Abstract This paper gives a model field-theoretic description of thermodynamic magnetization fluctuations and exchange interactions in localized ferromagnets and amorphous magnets. A local Ginzburg-Landau type Hamiltonian is used to describe the properties observed in the transition region. The approach provides another method of tackling interacting spin systems dominated by size effects, fluctuations and correlations, which lead to a dimensional phenomenology of critical behavior. It is also found that the competition between long- and short-range interactions gives rise to the redistribution of the density of spins and causes the anisotropy of the electron spectrum. Above the upper-critical dimension, the approach behaves like mean-field theory with however, thermodynamic quantities modified by intrinsic critical fluctuations, whereas it predicts correctly the universal quantities for dimension 4 and below. At all temperatures, the model matches the magnetic observables, thus providing a unified picture for both the Gaussian and critical regimes.

中文翻译：

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尺寸效应和交换相互作用的重整化高斯方法：在局部铁磁体和非晶磁体中的应用

摘要 本文给出了局部铁磁体和非晶磁体中热力学磁化波动和交换相互作用的模型场论描述。使用局部 Ginzburg-Landau 型哈密顿量来描述在过渡区域中观察到的性质。该方法提供了另一种处理由尺寸效应、波动和相关性主导的相互作用自旋系统的方法，这些自旋系统导致临界行为的维度现象学。还发现长程和短程相互作用之间的竞争引起自旋密度的重新分布并导致电子谱的各向异性。在上临界维度之上，该方法的行为类似于平均场理论，但是，热力学量由内在临界波动修改，而它正确预测了维度 4 及以下的通用量。在所有温度下，该模型都与磁观测值相匹配，从而为高斯和临界状态提供了统一的图片。