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:
“The male has been persuaded to assume a certain onerous and disagreeable rôle with the promise of rewards—material and psychological. Women may in the first place even have put it into his head. BE A MAN! may have been, metaphorically, what Eve uttered at the critical moment in the Garden of Eden.”
—Wyndham Lewis (1882–1957)
“The lifelong process of caregiving, is the ultimate link between caregivers of all ages. You and I are not just in a phase we will outgrow. This is life—birth, death, and everything in between.... The care continuum is the cycle of life turning full circle in each of our lives. And what we learn when we spoon-feed our babies will echo in our ears as we feed our parents. The point is not to be done. The point is to be ready to do again.”
—Paula C. Lowe (20th century)