Renormalization Group - Relevant and Irrelevant Operators, Universality Classes

Relevant and Irrelevant Operators, Universality Classes

Let us consider a certain observable of a physical system undergoing an RG transformation. The magnitude of the observable as the length scale of the system goes from small to large may be (a) always increasing, (b) always decreasing or (c) other. In the first case, the observable is said to be a relevant observable; in the second, irrelevant and in the third, marginal.

A relevant operator is needed to describe the macroscopic behaviour of the system; an irrelevant observable is not. Marginal observables may or may not need to be taken into account. A remarkable fact is that most observables are irrelevant, i.e.: the macroscopic physics is dominated by only a few observables in most systems. In other terms: microscopic physics contains (Avogadro's number) variables, and macroscopic physics only a few.

Before the RG, there was an astonishing empirical fact to explain: the coincidence of the critical exponents (i.e.: the behaviour near a second order phase transition) in very different phenomena, such as magnetic systems, superfluid transition (Lambda transition), alloy physics, etc. This was called universality and is successfully explained by RG, just showing that the differences between all those phenomena are related to irrelevant observables.

Thus, many macroscopic phenomena may be grouped into a small set of universality classes, described by the set of relevant observables.

See also: Dangerously irrelevant operator

Read more about this topic:  Renormalization Group

Famous quotes containing the words relevant, irrelevant and/or classes:

    Amongst the learned the lawyers claim first place, the most self-satisfied class of people, as they roll their rock of Sisyphus and string together six hundred laws in the same breath, no matter whether relevant or not, piling up opinion on opinion and gloss on gloss to make their profession seem the most difficult of all. Anything which causes trouble has special merit in their eyes.
    Desiderius Erasmus (c. 1466–1536)

    The last best hope of earth, two trillion dollars in debt, is spinning out of control, and all we can do is stare at a flickering cathode-ray tube as Ollie “answers” questions on TV while the press, resolutely irrelevant as ever, asks politicians if they have committed adultery. From V-J Day 1945 to this has been, my fellow countrymen, a perfect nightmare.
    Gore Vidal (b. 1925)

    Of all reformers Mr. Sentiment is the most powerful. It is incredible the number of evil practices he has put down: it is to be feared he will soon lack subjects, and that when he has made the working classes comfortable, and got bitter beer into proper-sized pint bottles, there will be nothing left for him to do.
    Anthony Trollope (1815–1882)