Nature of the onset of temperature chaos in spin glasses

Temperature chaos (TC) in spin glasses has been claimed to exist no matter how small the temperature change, ΔT. However, experimental studies exhibit a finite value of ΔT for the transition to TC. This work explores the onset of TC with higher accuracy over a large temperature (T) range. We obtained the native characteristic time, t_w,native^eff, by aging and measuring at the same T, and the temperature-changed characteristic time, t_w,T1→T2^eff, by aging at an initial T₁, and a reduced T₂, followed by measuring at T₂. With t_w,native^eff at T₁, we calculate the reversible characteristic time, t_R^eff, at each T₂, and the difference between t_w,T1→T2^eff and t_R^eff is the chaotic contribution, δ_TC. We find that TC is always present, though small, with δ_TC ~ 4% for the smallest ΔT = 0.05 K (T₁ = 18 K) in our experiments. It grows rapidly as ΔT increases, and the region of rapid growth coincides with the ΔT predicted from renormalization group arguments and observed experimentally. When t_R^eff is far beyond the laboratory time scale, t_w,T1→T2^eff reduces towards t_w,native^eff, and the difference between them, δ_C, decreases in an exponential manner becasue of the ultrametric symmetry for the hierarchical distribution of accessible states. δ_C reaches 0 when the spin glass has reached the completely chaotic state, and becomes negative as ΔT increases, resulting from the interference of its growth at T₂ with the frozen background created at T₁.