Post #2854385

#paperOfTheDay is "Criterion for Dominance of Directional over Size Fluctuations in Destroying Order" from 1999. This article is about statistical #physics , which can as an effective model also be described by #quantumFieldTheory . Many practically relevant statistical models live in D=3 or D=2 spacial dimensions, and they describe a quantity (called "order parameter") which is itself a vector with N components. It can be that N=D, but other situations are conceivable. At low temperature, such systems are usually in an "ordered" phase, where the O(N) rotation symmetry is broken. For example, in a Magnet, the small elementary magnets align and produce some non-zero macroscopic magnetic field. Even if the fundamental theory was agnostic with respect to vector orientations, the actual ground state has a preferred direction, the symmetry is "spontaneously broken". As the temperature increases, fluctuations increase, and eventually the symmetry is restored because all microscopic vectors are shuffled. One wants to know at which temperature this first happens, this is the critical temperature. An old estimate for the critical temperature was the "Ginzburg criterion", which is derived from the energy contribution of typical fluctuations in the magnitude of the field. The present article demonstrates that often, the "directional" fluctuations of the field are stronger than the magnitude fluctuations. This gives rise to a new, lower estimate of the critical temperature, the "Kleinert criterion". This nicely fits with the Goldstone theorem: The "angular" modes in the broken symmetry phase are massless, and thus more important for fluctuations than the massive "radial" mode. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.84.286