Scaling and Universality
One reason for the interest in phase transitions is scale invariance: the fluctuations that exist near the critical point occur on all possible length and time scales. A second reason for our interest is called universality: the striking similarity in behavior near the critical point among systems that are quite different from each other far from the critical point....
How can correlations actually extend an infinite distance away, without requiring a series of amplification stations all along the way? We can understand such “infinite-range propagation” as arising from the huge multiplicity of interaction paths that connect two atoms in dimensions greater than one. (In one dimension, there is no multiplicity of interaction paths, and atoms become aligned only at absolute zero temperature.)
How can correlations actually extend an infinite distance away, without requiring a series of amplification stations all along the way? We can understand such “infinite-range propagation” as arising from the huge multiplicity of interaction paths that connect two atoms in dimensions greater than one. (In one dimension, there is no multiplicity of interaction paths, and atoms become aligned only at absolute zero temperature.)
H. Eugene Stanley, L. A. N. Amaral, P. Gopikrishnan, P. Ch Ivanov, Timothy H. Keitt, and V. Plerou. "Scale invariance and universality: organizing principles in complex systems." Physica A: Statistical Mechanics and its Applications 281, no. 1-4 (2000): 60-68.
Full text: https://doi.org/10.1016/S0378-4371(00)00195-3
PDF: https://www.sciencedirect.com/science/article/pii/S0378437100001953/pdfft?isDTMRedir=true&download=true
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