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Sharp two- and three-dimensional phase transitional magnetization curves areobtained by an iterative renormalization-group coupling of Ising chains, whichare solved exactly. The chains by themselves do not have a phase transition ornon-zero magnetization, but the method reflects crossover from temperature-liketo field-like renormalization-group flows as the mechanism for thehigher-dimensional phase transitions. The magnetization of each chain acts, viathe interaction constant, as a magnetic field on its neighboring chains, thusentering its renormalization-group calculation. The method is highly flexiblefor wide application.

Across Dimensions: Two- and Three-Dimensional Phase Transitions from the Iterative Renormalization-Group Theory of Chains