Dynamic critical exponent z of the 3D Ising model
In plain words
Near the critical point a magnet relaxes very slowly, and the exponent z sets how the relaxation time grows with the size of correlated regions. For purely relaxational dynamics in three dimensions, z is known only approximately and has no exact theory.
Precise statement
For relaxational (model A, e.g. Glauber or Metropolis) dynamics in the 3D Ising universality class, determine $z$ in $\tau \sim \xi^z$ to precision $10^{-4}$ or better. The best Monte Carlo estimate is $z = 2.0245(15)$ from the improved Blume-Capel model (arXiv:1908.01702), and the five-loop $\epsilon$ expansion gives $z = 2.0235(8)$ (arXiv:2111.04719).
What would settle it
An independent high-precision Monte Carlo study or a dynamical bootstrap or RG computation reaching $10^{-4}$ accuracy with controlled corrections to scaling.
Status in the literature
Unverified note
Monte Carlo gives $z = 2.0245(15)$ (arXiv:1908.01702) and the five-loop epsilon expansion gives $z = 2.0235(8)$ (arXiv:2111.04719, 2021), consistent within errors; $z \ge 2$ was proven for Glauber dynamics in 2025 (arXiv:2502.09908).