2003/04/22 by Grégory Schehr, Gregory Schehr, Pierre Le Doussal · 1 citation
Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Quantum many-body systems #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physreve.68.046101
published as Phys.Rev. E68 (2003) 046101 · 33 pages, RevTex
arxiv created 2003/04/22 · openalex publication_date 2003/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal parts yields a closed exact RG equation for the local part, to a given order in the local part. The method is illustrated on the O(N) model by straightforwardly recovering the eta exponent and scaling functions. Then it is applied to study the glass phase of the Cardy-Ostlund, random phase sine Gordon model near the glass transition temperature. The static correlations and equilibrium dynamical exponent z are recovered and several results are obtained, such as the equilibrium two-point scaling functions. The nonequilibrium, finite momentum, two-time t,t' response and correlations are computed. They are shown to exhibit scaling forms, characterized by exponents lambda(R) not equal lambda(C), as well as universal scaling functions that we compute. The fluctuation dissipation ratio is found to be nontrivial and of the form X[q(z)(t-t'),t/t']. Analogies and differences with pure critical models are discussed.