2021/12/02 by Nathan O. Silvano, Silvano, Nathan O., Daniel G. Barci +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2112.01547
openalex publication_date 2021/12/02 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
We study the critical dynamics of a real scalar field in two dimensions near a continuous phase transition. We have built up and solved Dynamical Renormalization Group equations at one-loop approximation. We have found that, different form the case d\lesssim 4, characterized by a Wilson-Fisher fixed point with dynamical critical exponent z=2+ O(ε2), the critical dynamics is dominated by a novel multiplicative noise fixed point. The zeroes of the beta function depend on the stochastic prescription used to define the Wiener integrals. However, the critical exponents and the anomalous dimension do not depend on the prescription used. Thus, even though each stochastic prescription produces different dynamical evolutions, all of them are in the same universality class.