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universality
interesting what is regarded as leadership - a greater than perspective - truly a different world - on how much fun the word is when all disciplines are in balance - this teknique we have been using verifies how easy it is to keep a balance on singular and mass communications - if you are in acceptance of the dispatch and feel it flos freely then we have collectively xperienced the effect of its potential - with the advent of the symmetrical 2 way net phenomena it allows others to network without mis interpretation of intention - in detail let us consider a certain observable A of a physical system undergoing an RG transformation - the magnitude of the observable as the 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 renormalization group (RG) a relevant operator is needed to describe the macroscopic behaviour of the system, but not an irrelevant observable.. marginal observables always give trouble when deciding whether to take them into account or not... 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 10 to the 23 power 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, alloy physics... 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 re-entry by renormalization renormalization group (RG) refers to a set of techniques and concepts related to the change of physics with the observation scale it is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents... this phenomenon is known as universality - for example, the critical exponents at the liquid-gas critical point have been found to be independent of the chemical composition of the fluid... more amazingly, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets... such systems are said to be in the same universality class - universality is a prediction of the renormalization group theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and is insensitive to the underlying microscopic properties of the system so we have relevant operators creating a renormalization group empowering universality classes thru a phase transition of dimensionality and symmetry - sndz like us the djed report - continued the djed report neu ark net / ark lite / ios |