# Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models

## Abstract

We calculate the corrections to the thermodynamic limit of the critical density for jamming in the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models, and find them to be finite-density corrections, and not finite-size corrections. We do this by introducing a new numerical algorithm, which requires negligible computer memory since contrary to alternative approaches, it generates at each point only the necessary data. The algorithm starts from a single unfrozen site and at each step randomly generates the neighbors of the unfrozen region and checks whether they are frozen or not. Our results correspond to systems of size greater than 10{sup 7} × 10{sup 7}, much larger than any simulated before, and are consistent with the rigorous bounds on the asymptotic corrections. We also find that the average number of sites that seed a critical droplet is greater than 1.

- Authors:

- School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

- Publication Date:

- OSTI Identifier:
- 22420014

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DENSITY; DROPLETS; SIMULATION

### Citation Formats

```
Teomy, Eial, E-mail: eialteom@post.tau.ac.il, and Shokef, Yair, E-mail: shokef@tau.ac.il.
```*Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models*. United States: N. p., 2014.
Web. doi:10.1063/1.4892416.

```
Teomy, Eial, E-mail: eialteom@post.tau.ac.il, & Shokef, Yair, E-mail: shokef@tau.ac.il.
```*Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models*. United States. doi:10.1063/1.4892416.

```
Teomy, Eial, E-mail: eialteom@post.tau.ac.il, and Shokef, Yair, E-mail: shokef@tau.ac.il. Thu .
"Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models". United States.
doi:10.1063/1.4892416.
```

```
@article{osti_22420014,
```

title = {Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models},

author = {Teomy, Eial, E-mail: eialteom@post.tau.ac.il and Shokef, Yair, E-mail: shokef@tau.ac.il},

abstractNote = {We calculate the corrections to the thermodynamic limit of the critical density for jamming in the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models, and find them to be finite-density corrections, and not finite-size corrections. We do this by introducing a new numerical algorithm, which requires negligible computer memory since contrary to alternative approaches, it generates at each point only the necessary data. The algorithm starts from a single unfrozen site and at each step randomly generates the neighbors of the unfrozen region and checks whether they are frozen or not. Our results correspond to systems of size greater than 10{sup 7} × 10{sup 7}, much larger than any simulated before, and are consistent with the rigorous bounds on the asymptotic corrections. We also find that the average number of sites that seed a critical droplet is greater than 1.},

doi = {10.1063/1.4892416},

journal = {Journal of Chemical Physics},

number = 6,

volume = 141,

place = {United States},

year = {Thu Aug 14 00:00:00 EDT 2014},

month = {Thu Aug 14 00:00:00 EDT 2014}

}