### Information-entropic signature of the critical point

Here, we investigate the critical behavior of continuous (second-order) phase transitions in the context of (2 + 1)-dimensional Ginzburg–Landau models with a double-well effective potential. In particular, we show that the recently-proposed configurational entropy (CE)—a measure of the spatial complexity of the order parameter in momentum space based on its Fourier-mode decomposition—can be used to identify the critical point. We compute the CE for different temperatures and show that large spatial fluctuations near the critical point (

*T*_{c})—characterized by a divergent correlation length—lead to a sharp decrease in the associated configurational entropy. We further show that the CE density goes from a scale-free to an approximate scaling behavior |k|^{–5/3}as the critical point is approached. As a result, we reproduce the behavior of the CE at criticality with a percolating many-bubble model.- Publication Date:

- Grant/Contract Number:
- SC0010386

- Type:
- Published Article

- Journal Name:
- Physics Letters. Section B

- Additional Journal Information:
- Journal Volume: 747; Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Research Org:
- Dartmouth College, Hanover, NH (United States)

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING

- OSTI Identifier:
- 1209772

- Alternate Identifier(s):
- OSTI ID: 1457029

```
Gleiser, Marcelo, and Sowinski, Damian.
```*Information-entropic signature of the critical point*. United States: N. p.,
Web. doi:10.1016/j.physletb.2015.05.058.

```
Gleiser, Marcelo, & Sowinski, Damian.
```*Information-entropic signature of the critical point*. United States. doi:10.1016/j.physletb.2015.05.058.

```
Gleiser, Marcelo, and Sowinski, Damian. 2015.
"Information-entropic signature of the critical point". United States.
doi:10.1016/j.physletb.2015.05.058.
```

```
@article{osti_1209772,
```

title = {Information-entropic signature of the critical point},

author = {Gleiser, Marcelo and Sowinski, Damian},

abstractNote = {Here, we investigate the critical behavior of continuous (second-order) phase transitions in the context of (2 + 1)-dimensional Ginzburg–Landau models with a double-well effective potential. In particular, we show that the recently-proposed configurational entropy (CE)—a measure of the spatial complexity of the order parameter in momentum space based on its Fourier-mode decomposition—can be used to identify the critical point. We compute the CE for different temperatures and show that large spatial fluctuations near the critical point (Tc)—characterized by a divergent correlation length—lead to a sharp decrease in the associated configurational entropy. We further show that the CE density goes from a scale-free to an approximate scaling behavior |k|–5/3 as the critical point is approached. As a result, we reproduce the behavior of the CE at criticality with a percolating many-bubble model.},

doi = {10.1016/j.physletb.2015.05.058},

journal = {Physics Letters. Section B},

number = C,

volume = 747,

place = {United States},

year = {2015},

month = {5}

}