Fig. 3: Relaxation frequency and effective temperature of the critical active system.
From: Critical active dynamics is captured by a colored-noise driven field theory
a Peak frequency \({\omega }_{\max }\) of the correlator (circles) and of the response (squares) as a function of q. Error-bars represent the fit error on the peak position. Different colors indicate different systems sizes (see legend). The straight full line is a power-law fit of the low-q correlator peak-frequencies (i.e. the yellow points for which N = 60 × 103), yielding a critical exponent z very close to the Ising one (z = 3.75), which is lower than the mean-field value (the best fit with z = 4 is indicated by the dashed line). The inset (same axes as the main panel) shows the peak frequency for the equilibrium triangular lattice gas. Deviations from the scaling \({\omega }_{\max } \sim {q}^{4}\) are also found at high q-values. b Effective temperature evaluated at the correlator peak-frequency \({T}_{{{{{{{{\rm{eff}}}}}}}}}{(q,\omega )}_{\max }\) as a function of q (different colors indicate different system sizes with the same as in a. Error-bars represent the linear propagation of the error on the peak amplitude. The black curve is a fit of the low-q data by means of the expression found in the one-loop colored-noise-driven field theory (Eq. (11)). c Frequency resolved effective temperature Teff(q, ω) in the low-q regime (colored curves), different colors indicate different q-values (see legend). The dashed line represents the power-law ω−2 predicted by the theory for asymptotic behavior of Teff. The inset shows \(\ln [{T}_{{{{{{{{\rm{eff}}}}}}}}}(q,\omega )]\) as color map (value increasing from blue to orange) at all q and ω-s. The gray area represents the highest and lowest ω measured at each q determined by the simulation duration and sampling frequency. The dashed black lines indicate the of low q-values range selected for the main panel. d Data in c are scaled according to the theory. Collapsed data are well fitted by the Lorentzian predicted by the theory (full line). The inset is the same of the inset of c but for the scaled effective temperature appearing in the main panel.
