Sharp two- and three-dimensional phase transitional magnetization curves are obtained by an iterative renormalization-group coupling of Ising chains, which are solved exactly. The chains by themselves do not have a phase transition or nonzero magnetization, but the method reflects crossover from temperaturelike to fieldlike renormalization-group flows as the mechanism for the higher-dimensional phase transitions. The magnetization of each chain acts, via the interaction constant, as a magnetic field on its neighboring chains, thus entering its renormalization-group calculation. The method is highly flexible for wide application.

中文翻译：

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跨维度：来自链的迭代重整化组理论的二维和三维相变

通过对伊辛链进行重归一化迭代迭代，可以得到清晰的二维和三维相变磁化曲线。链本身没有相变或非零磁化强度，但该方法反映了从温度到场的重归一化组流的交叉，这是高维相变的机制。每个链的磁化强度通过相互作用常数充当相邻链上的磁场，从而进入重归一化组计算。该方法具有高度的灵活性，可以广泛应用。