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

Abstract

We explicitly demonstrate the universality of critical dynamics through unprecedented large-scale 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 $10^3$ lattice spacings. Finite-size effects are negligible due to the mesoscopic scale of the lattice sizes studied, with linear dimensions up to $L=2^{22}$ and $2^{19}$ 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 \emph{above} the critical temperature, through a time-dependent variation of the thermal bath temperature. The results presented in this work leverage our CUDA-based numerical code, breaking the world record for the simulation speed of the Ising model.

10 pages, 8 figures, 2 tables, appendix included as supplementary material, version accepted for publication in Physical Review Research

References in corpus (13)

• Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
• Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
• Eigenvalue crossing as a phase transition in relaxation dynamics
• Shortcuts of freely relaxing systems using equilibrium physical observables
• Memory and rejuvenation in spin glasses: aging systems are ruled by more than one length scale
• Testing statics-dynamics equivalence at the spin-glass transition in three dimensions
• The dynamic critical exponent $z$ for 2d and 3d Ising models from five-loop $\epsilon$ expansion
• Relaxational dynamics in 3D randomly diluted Ising models
• Critical dynamical behavior of the Ising model
• The QISG suite: high-performance codes for studying Quantum Ising Spin Glasses
• Critical relaxational dynamics at the continuous transitions of three-dimensional spin models with ${\mathbb{Z}}_2$ gauge symmetry
• Quantifying memory in spin glasses
• Massive-Scale Simulations of 2D Ising and Blume-Capel Models on Rack-Scale Multi-GPU Systems

Cited by in corpus (2)

• Pontus-Mpemba effects
• Phase transition properties via partition function zeros: The Blume-Capel ferromagnet revisited