Normal form for renormalization groups
Autor: | Colin B. Clement, Archishman Raju, James P. Sethna, Danilo B. Liarte, D. Zeb Rocklin, Lorien X. Hayden, Jaron Kent-Dobias |
---|---|
Rok vydání: | 2017 |
Předmět: |
Statistical Mechanics (cond-mat.stat-mech)
Near critical General Physics and Astronomy FOS: Physical sciences 16. Peace & justice 01 natural sciences 010305 fluids & plasmas Renormalization 0103 physical sciences Normal form theory Statistical physics 010306 general physics Condensed Matter - Statistical Mechanics Mathematics Fractal systems |
DOI: | 10.48550/arxiv.1706.00137 |
Popis: | The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a case-by-case basis. We use the mathematics of normal form theory to systematically group these into universality families of seemingly unrelated systems united by common scaling variables. We recover and explain the existing literature and predict the nonlinear generalization for the universal homogeneous scaling functions. We show that this procedure leads to a better handling of the singularity even in classic cases and elaborate our framework using several examples. |
Databáze: | OpenAIRE |
Externí odkaz: |