Exemplary results for deterministic and stochastic numerical solutions to the ferromagnetic-paramagnetic phase transition problem of magnetic materials.

The data is not restricted and has already been published in the literature through technical papers.

This dataset is associated with two publications:

E. Eger and P. Acar, "Uncertainty Quantification of Phase Transitions in Magnetic Materials Lattices", *Applied Physics Letters*, Vol. 124, 020501, January 2024; doi:10.1063/5.0183844

E. Eger and P. Acar, "Uncertainty Analysis for Ferromagnetic-Paramagnetic Phase Transition Behavior of Magnetic Materials"**, ***JOM*, *accepted for publication*, 2024**.**

## Publisher

University Libraries, Virginia Tech## Corresponding Author Name

Pinar Acar## Files/Folders in Dataset and Description

[Magnetization Data]
[Deterministic] Include deterministic results for the phase transition problem
[H_and_T_Uncertainty] Include stochastic results when external field and temperature are random variables
[H_Uncertainty] Include stochastic results when the external field is a random variable
[T_Uncertainty] Include stochastic results when the temperature is a random variable
[Example.py] The main file that generates the figures
Naming convention of files & folders: There are 4 files, Deterministic, H_Uncertainty, T_Uncertainty and H_and_T_Uncertainty.
Files in Deterministic folders are generated for differen k_BT (Boltzmann Constant*Temperature) and h (External Field) whose values follow the corresponding parameter. These values are generated for every combination in the domain (2^(4x4), they match the magnetization values in the Magnetization.npy file. Use of these values are shared in the Example.py, particularly to generate magnetization versus normalized free energy curve.
For example Deterministic->KBT33H05.npy file has the free energy of all of the combinations under k_BT=3.3 and h=0.5
Files in H_Uncertainty, T_Uncertainty and H_and_T_Uncertainty, contain the free energy values that are generated with values of the parameters h only, k_BT only, and both of them together based on the Gaussion distribution. They are applied on a certain combination, particularly the one matching the minimum of free energy magnetization curve. Also the combination id that is used is given in the final portion in the naming. The mean values of parameters are given in the same way as in Deterministic folder. Use of these values are shared in the Example.py, particularly to generate free energy distribution.
For example H_Uncertainty->KBT29H003_H_UNCcomb6232.npy file has the free energy of the combination 6232 under constant k_BT=3.3 and varying h with mean=0.5,