Dataset Open Access

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

Miguel Aguilera

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    <subfield code="a">&lt;p&gt;Datasets for reproducing the results in the article Aguilera, M., Moosavi, S.A. &amp;amp; Shimazaki, H. A unifying framework for mean-field theories of asymmetric kinetic Ising systems. &lt;em&gt;Nature Communications&lt;/em&gt; &lt;strong&gt;12, &lt;/strong&gt;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&lt;/p&gt;

&lt;p&gt;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&amp;nbsp;&lt;span class="math-tex"&gt;\(H_i\)&lt;/span&gt; are sampled from independent uniform distributions &lt;span class="math-tex"&gt;\(\mathcal{U}(-\beta H_0, \beta H_0)\)&lt;/span&gt; with &lt;span class="math-tex"&gt;\(H_0=0.5\)&lt;/span&gt;, whereas coupling terms&amp;nbsp;&lt;span class="math-tex"&gt;\(J_{ij}\)&lt;/span&gt; are sampled from independent Gaussian distributions &lt;span class="math-tex"&gt;\(\mathcal{N}(\beta \frac{J_0}{N},\beta^2 \frac{J_\sigma^2}{N})\)&lt;/span&gt;, with&amp;nbsp;&lt;span class="math-tex"&gt;\(J_0=1, J_\sigma = 0.1\)&lt;/span&gt; where &lt;span class="math-tex"&gt;\(\beta\)&lt;/span&gt; is a scaling parameter (i.e., an inverse temperature).&lt;/p&gt;

&lt;p&gt;To study the non-stationary transient dynamics of the model, we start from&amp;nbsp;&lt;span class="math-tex"&gt;\(\mathbf s_0 = \mathbf 1\)&lt;/span&gt; (all elements set to 1 at &lt;span class="math-tex"&gt;\(t=0\)&lt;/span&gt;) and recursively update its state for &lt;span class="math-tex"&gt;\(T=128\)&lt;/span&gt; steps. We repeated this stochastic simulation for &lt;span class="math-tex"&gt;\(10^6\)&lt;/span&gt; trials for 21 values of&amp;nbsp;&lt;span class="math-tex"&gt;\(\beta\)&lt;/span&gt; in the range &lt;span class="math-tex"&gt;\([0.7\beta_c, 1.3\beta_c]\)&lt;/span&gt;, except for the reconstruction of the phase transition where we used&amp;nbsp;&lt;span class="math-tex"&gt;\(R=10^5\)&lt;/span&gt; and 201 values of &lt;span class="math-tex"&gt;\(\beta\)&lt;/span&gt; in the same range.&lt;br&gt;
&lt;br&gt;
Each file is stored in: &amp;#39;data-H0-0.5-J0-1.0-Js-0.1-N-512-R-1000000-beta-[beta_ref].npz&amp;#39;, where [beta_ref] contains the normalized value of &lt;span class="math-tex"&gt;\(\beta/\beta_C\)&lt;/span&gt; between 0.7 and 1.3.&lt;br&gt;
&lt;br&gt;
Furthermore, data in the folders &amp;#39;forward.zip&amp;#39;, &amp;#39;inverse.zip&amp;#39; and &amp;#39;reconstruction.zip&amp;#39; 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.&lt;/p&gt;</subfield>
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December 12, 2020
DOI:
10.5281/zenodo.4318983

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Nature Communications: 12 (1197).
Grants:
European Commission:
  • MSCA 2018 - Marie Skłodowska-Curie Actions - Beyond 2020 (811208)
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