We consider the d -dimensional transverse-field Ising model with power-law interactions J /rd +σ 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 κ and distances longer than a (J/κ ) 2 /σ 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 θ =1 and dynamical critical exponent z =σ /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.
Physical Review B
- Pub Date:
- July 2018
- Condensed Matter - Strongly Correlated Electrons;
- Condensed Matter - Statistical Mechanics;
- Quantum Physics
- Accepted version, 11 pages, 5 figures