2018/03/31 by Jad C. Halimeh, Matthias Punk, Francesco Piazza
Mathematics · Physics and Astronomy · #Condensed matter physics #Critical exponent #Exponent #Ising model #Magnetic field #Magnetization #Mathematics #Opinion Dynamics and Social Influence #Physics #Quantum many-body systems #Quantum mechanics #Renormalization group #Scaling #Sigma #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.98.045111
published as Phys. Rev. B 98, 045111 (2018) · Accepted version, 11 pages, 5 figures
arxiv created 2018/06/28 · openalex publication_date 2018/07/06 · arxiv updated 2018/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the d-dimensional transverse-field Ising model with power-law interactions J/r^d+\ensuremathσ in the presence of a noisy longitudinal field with zero average. We study the longitudinal-magnetization dynamics of an initial paramagnetic state after a sudden switch-on of both the interactions and the noisy field. While the system eventually relaxes to an infinite-temperature state with vanishing magnetization correlations, we find that two-time correlation functions show aging at intermediate times. Moreover, for times shorter than the inverse noise strength \ensuremathκ and distances longer than a(J/\ensuremathκ)^2/\ensuremathσ with a being the lattice spacing, we find a critical scaling regime of correlation and response functions consistent with the model A dynamical universality class with an initial-slip exponent \ensuremathθ=1 and dynamical critical exponent z=\ensuremathσ/2. We obtain our results analytically by deriving an effective action for the magnetization field including the noise in a nonperturbative way. The above scaling regime is governed by a nonequilibrium fixed point dominated by the noise fluctuations.