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
Famous quotes containing the words critical and/or point:
“His misfortune was that he loved youth—he was weak to it, it kindled him. If there was one eager eye, one doubting, critical mind, one lively curiosity in a whole lecture-room full of commonplace boys and girls, he was its servant. That ardour could command him. It hadn’t worn out with years, this responsiveness, any more than the magnetic currents wear out; it had nothing to do with Time.”
—Willa Cather (1873–1947)
“Any historian of the literature of the modern age will take virtually for granted the adversary intention, the actually subversive intention, that characterizes modern writing—he will perceive its clear purpose of detaching the reader from the habits of thought and feeling that the larger culture imposes, of giving him a ground and a vantage point from which to judge and condemn, and perhaps revise, the culture that produces him.”
—Lionel Trilling (1905–1975)