A unifying framework for mean-field theories of asymmetric kinetic Ising systems [Dataset]

Datasets for reproducing the results in the article Aguilera, M., Moosavi, S.A. & Shimazaki, H. A unifying framework for mean-field theories of asymmetric kinetic Ising systems. Nature Communications 12, 1197 (2021). https://doi.org/10.1038/s41467-021-20890-5. Results can be reproduced using the code repository of the article https://github.com/MiguelAguilera/kinetic-Plefka-expansions

The main dataset contains simulations of an asymmetric, kinetic Sherrington-Kirkpatrick (SK) model around the equivalent of a ferromagnetic phase transition in the equilibrium SK model. External fields \(H_i\) are sampled from independent uniform distributions \(\mathcal{U}(-\beta H_0, \beta H_0)\) with \(H_0=0.5\), whereas coupling terms \(J_{ij}\) are sampled from independent Gaussian distributions \(\mathcal{N}(\beta \frac{J_0}{N},\beta^2 \frac{J_\sigma^2}{N})\), with \(J_0=1, J_\sigma = 0.1\) where \(\beta\) is a scaling parameter (i.e., an inverse temperature).

To study the non-stationary transient dynamics of the model, we start from \(\mathbf s_0 = \mathbf 1\) (all elements set to 1 at \(t=0\)) and recursively update its state for \(T=128\) steps. We repeated this stochastic simulation for \(10^6\) trials for 21 values of \(\beta\) in the range \([0.7\beta_c, 1.3\beta_c]\), except for the reconstruction of the phase transition where we used \(R=10^5\) and 201 values of \(\beta\) in the same range.

Each file is stored in: 'data-H0-0.5-J0-1.0-Js-0.1-N-512-R-1000000-beta-[beta_ref].npz', where [beta_ref] contains the normalized value of \(\beta/\beta_C\) between 0.7 and 1.3.

Furthermore, data in the folders 'forward.zip', 'inverse.zip' and 'reconstruction.zip' contain files to reproduce the results of the paper above. These files show the results of solving the forward Ising problem, the inverse Ising problem, and the reconstruction of the phase transition combining forward and inverse problems.