Universal exotic dynamics in critical mesoscopic systems: Simulating the square root of Avogadro’s number of spins

We explicitly demonstrate the universality of critical dynamics through unprecedented large-scale Graphics Processing Units (GPU)-based simulations of two out-of-equilibrium processes, comparing the behavior of spin-1/2 Ising and spin-1 Blume-Capel models on a square lattice. In the first protocol, a completely disordered system is instantaneously brought into contact with a thermal bath at the critical temperature, allowing it to evolve until the coherence length exceeds 103 lattice spacings. Finite-size effects are negligible due to the mesoscopic scale of the lattice sizes studied, with linear dimensions up to 𝐿=222 and 219 for the Ising and Blume-Capel models, respectively. Our numerical data, and the subsequent analysis, demonstrate a strong dynamic universality between the two models and provide the most precise estimate to date of the dynamic critical exponent for this universality class, 𝑧=2.1676⁢(1). In the second protocol, we corroborate the role of the universal ratio of dynamic and static length scales in achieving an exponential acceleration in the approach to equilibrium just above the critical temperature, through a time-dependent variation of the thermal bath temperature. The results presented in this work leverage our Compute Unified Device Architecture (CUDA)-based numerical code, breaking the world record for the simulation speed of the Ising model.