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Title: Information-entropic signature of the critical point

Abstract

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.

Authors:
 [1];  [1]
  1. Dartmouth College, Hanover, NH (United States)
Publication Date:
Research Org.:
Dartmouth College, Hanover, NH (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1209772
Alternate Identifier(s):
OSTI ID: 1457029
Grant/Contract Number:  
SC0010386
Resource Type:
Journal Article: Published Article
Journal Name:
Physics Letters. Section B
Additional Journal Information:
Journal Volume: 747; Journal Issue: C; Journal ID: ISSN 0370-2693
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING

Citation Formats

Gleiser, Marcelo, and Sowinski, Damian. Information-entropic signature of the critical point. United States: N. p., 2015. 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. Wed . "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},
issn = {0370-2693},
number = C,
volume = 747,
place = {United States},
year = {2015},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.physletb.2015.05.058

Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

Figures / Tables:

Fig. 1 Fig. 1: (Color online.) The order parameter 〈X〉 [top (blue) line] and the volume fraction (pV ) occupied by the X > 0 phase [bottom (green) line] vs. temperature. The shaded regions correspond to 1σ deviations from the mean. Within the accuracy of our simulation, the critical temperature is θcmore » ≃0.43 ± .01, marked by the vertical band.« less

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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.