Divergences At The Critical Point
The correlation length diverges at the critical point: as, . This divergence poses no physical problem. Other physical observables diverge at this point, leading to some confusion at the beginning.
The most important is susceptibility. Let us apply a very small magnetic field to the system in the critical point. A very small magnetic field is not able to magnetize a large coherent cluster, but with these fractal clusters the picture changes. It affects easily the smallest size clusters, since they have a nearly paramagnetic behaviour. But this change, in its turn, affects the next-scale clusters, and the perturbation climbs the ladder until the whole system changes radically. Thus, critical systems are very sensitive to small changes in the environment.
Other observables, such as the specific heat, may also diverge at this point. All these divergences stem from that of the correlation length.
Read more about this topic: Critical Phenomena
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