Critical exponents from power spectra

J. C. Le Guillou, Jean Zinn‐Justin

Kwan-tai Leung

We consider power spectra for fluctuating quantities at a critical point, P( omega ) varies as omega - phi , where phi is determined by the dynamic exponent z and static exponents specific to the quantity considered. From the magnetization spectra obtained with simulations, z is found to be 2.13+or-0.03 for the two-dimensional Glauber kinetic Ising model, hence in accord with recent Monte Carlo relaxational studies, but at odds with those obtained by series expansion and damage spreading methods. Excellent dynamic finite-size scaling for system sizes L=10 to 128 supports our estimate.

V. A. Rabinovich, Yu. E. Sheludyak

Zhi Chen, Clare C. Yu

We provide a general scheme to predict and derive the contribution to the noise spectrum of a stochastic sequence of pulses from the distribution of pulse parameters. An example is the magnetization noise spectra of a two-dimensional Ising system near its phase transition. At $T\ensuremath{\le}{T}_{c}$, the low-frequency spectra is dominated by magnetization flips of nearly the entire system. We find that both the predicted and the analytically derived spectra fit those produced from simulations. Subtracting this contribution at ${T}_{c}$ leaves the high-frequency spectra which follow a power law determined by the critical exponents.

Steven Mathey, Sebastian Diehl

This paper shows that the slow drive that triggers the Kibble-Zurek mechanism can be used to activate not only the leading critical exponents of the underlying equilibrium problem, but the full critical exponent spectrum. This uncovers a new aspect of the Kibble-Zurek phenomenology, where the underlying equilibrium critical physics provides multiple universal scaling regimes.

Andrew S. Hirsch