DOI: 10.5281/zenodo.17966995
title: Equilibrium samples from Inverse Power Law and Kob-Andersen glassy systems

description: This dataset contains equilibrium particle configurations generated via Metropolis–Hastings Monte Carlo simulations for two model glass-forming systems: the Inverse Power Law (IPL) system and the Kob–Andersen (KA) system. The configurations were produced to serve as training data for data-driven and statistical analyses of interacting particle systems.

Dataset generation

The simulations were performed using the Metropolis-Hastings Monte Carlo algorithm. Each simulation starts from particles uniformly distributed within a two-dimensional periodic box. At each Monte Carlo step, one particle is selected uniformly at random and a trial displacement is proposed, drawn from a Gaussian distribution centered at the particle’s current position with standard deviation $0.065$. The proposed move is accepted or rejected according to the standard Metropolis criterion. One unit of time corresponds to $N$ attempted particle moves, where $N$ is the number of particles in the system.

For each dataset, 100 independent Monte Carlo chains were initialized from different random configurations and evolved for 10⁴ time units to ensure equilibration. On this timescale, the potential energy relaxes to a steady value and the self-intermediate scattering function decays to zero, confirming that the system has reached equilibrium. From these equilibrated states, each chain was further propagated for an additional 10⁷ time units. Particle configurations were stored every 10⁴ time units, yielding a total of 10⁵ statistically uncorrelated equilibrium configurations, which constitute the dataset.

For the KA system at the lowest temperature ($T = 0.32$), the Gaussian displacement moves were augmented with swap moves [Ninarello et al., 2017]. With probability $p_{\text{swap}}$, a swap move was proposed by selecting two particles of different species uniformly at random and exchanging their species labels. The proposal was accepted or rejected according to the standard Metropolis criterion. Swap moves are known to dramatically accelerate equilibration in this system [Jung et al., 2024].

Interaction potentials

For both systems, the total potential energy of a configuration $X = (X_1,\dots,X_N)$ with species labels $s = (s_1,\dots,s_N)$ is$$\mathrm{U}(s, X) = \sum_{i=1}^N \sum_{j<i}^N \mathrm{W}\left(s_i, s_j, \mathrm{d}_{L}(X_i, X_j)\right),$$where $d_L$ denotes the distance on the two-dimensional periodic torus of length $L > 0$.

Inverse Power Law (IPL) system. The pairwise interaction potential is $$\mathrm{W}_{\mathrm{IPL}}(s_1, s_2, r) = \epsilon \left(\frac{\sigma_{s_1 s_2}}{r}\right)^{12} + \mathrm{W}_0$$ with a cutoff at $r = 2.5 \sigma_{s_1, s_2}$. We set $(\sigma_{00}, \sigma_{01}, \sigma_{10} \sigma_{11}) = (1.0,1.2, 1.2, 1.4)$ and $\epsilon = 1$. The constant $\mathrm{W}_0$ is chosen such that the potential is continuous at the cutoff.

Kob-Andersen (KA) system. The pairwise interaction potential is $$\mathrm{W}_{\mathrm{KA}}(s_1, s_2, r) = \mathrm{W}_{\mathrm{LJ}}(r; \epsilon_{s_1 s_2}, \sigma_{s_1 s_2}) + \mathrm{W}_0 + \mathrm{W}_2 \left(\frac{r}{\sigma_{s_1 s_2}}\right)^2 + \mathrm{W}_4 \left(\frac{r}{\sigma_{s_1 s_2}}\right)^4$$ where $\mathrm{W}_{\mathrm{LJ}}$ is the Lennard-Jones potential. We also apply a cutoff at $r = 2.5 \sigma_{s_1, s_2}$. The correction terms $\mathrm{W}_0, \mathrm{W}_2, \mathrm{W}_4$ are chosen as in [Jung et al., 2024] to ensure smoothness of the potential at the cutoff. The values of $\epsilon$ and $\sigma$ are the same as [Jung et al., 2024].

Systems and simulation parameters





Dimensionality: $d = 2$




Simulation box: square with periodic boundary conditions $L = \left(\frac{N}{\rho}\right)^{1/d}$




Target densities:





IPL system: $\rho = 0.5$




KA system: $\rho = 1.1920748468939728$





File contents and naming convention

For each system, temperature, and particle number, the dataset provides:





Particle positions (PyTorch tensor of shape (100000, $N$, $d$)):

[SYSTEM_TYPE][N]_T[TEMPERATURE]_positions.pt





Particle species (PyTorch tensor of shape (100000, $N$), integer labels):

[SYSTEM_TYPE][N]_T[TEMPERATURE]_species.pt




where:





SYSTEM_TYPE is ipl (Inverse Power Law) or ka (Kob–Andersen),




N is the number of particles,




TEMPERATURE is the simulation temperature.



Each positions file contains particle coordinates within the periodic simulation box, and the corresponding species file specifies particle identities consistent with the interaction parameters of the system.

Intended use

This dataset is intended for research on equilibrium properties of interacting particle systems, including machine learning applications, statistical mechanics analyses, and studies of glass-forming liquids.