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Microcanonical entropy of the infinite-state potts model

Johansson, Jonas LU orcid and Pistol, Mats Erik LU (2011) In Physics Research International 2011.
Abstract

In this investigation we show that the entropy of the two-dimensional infinite-state Potts model is linear in configurational energy in the thermodynamic limit. This is a direct consequence of the local convexity of the microcanonical entropy, associated with a finite system undergoing a first-order transition. For a sufficiently large number of states q, this convexity spans the entire energy range of the model. In the thermodynamic limit, the convexity becomes insignificant, and the microcanonical entropy (the logarithm of the density of states) tends to a straight line. In order to demonstrate the behaviour of the convexity, we use the Wang-Landau Monte-Carlo technique to numerically calculate the density of states for a few finite... (More)

In this investigation we show that the entropy of the two-dimensional infinite-state Potts model is linear in configurational energy in the thermodynamic limit. This is a direct consequence of the local convexity of the microcanonical entropy, associated with a finite system undergoing a first-order transition. For a sufficiently large number of states q, this convexity spans the entire energy range of the model. In the thermodynamic limit, the convexity becomes insignificant, and the microcanonical entropy (the logarithm of the density of states) tends to a straight line. In order to demonstrate the behaviour of the convexity, we use the Wang-Landau Monte-Carlo technique to numerically calculate the density of states for a few finite but high values of q. Finally, we calculate the free energy and discuss the generality of our results.

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author
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publishing date
type
Contribution to journal
publication status
published
subject
in
Physics Research International
volume
2011
article number
437093
publisher
Hindawi Limited
external identifiers
  • scopus:84855597157
ISSN
1687-689X
DOI
10.1155/2011/437093
language
English
LU publication?
yes
id
12abb20b-50ff-47b5-b089-44260d1a28ba
date added to LUP
2022-04-25 09:10:27
date last changed
2023-09-25 02:02:40
@article{12abb20b-50ff-47b5-b089-44260d1a28ba,
  abstract     = {{<p>In this investigation we show that the entropy of the two-dimensional infinite-state Potts model is linear in configurational energy in the thermodynamic limit. This is a direct consequence of the local convexity of the microcanonical entropy, associated with a finite system undergoing a first-order transition. For a sufficiently large number of states q, this convexity spans the entire energy range of the model. In the thermodynamic limit, the convexity becomes insignificant, and the microcanonical entropy (the logarithm of the density of states) tends to a straight line. In order to demonstrate the behaviour of the convexity, we use the Wang-Landau Monte-Carlo technique to numerically calculate the density of states for a few finite but high values of q. Finally, we calculate the free energy and discuss the generality of our results.</p>}},
  author       = {{Johansson, Jonas and Pistol, Mats Erik}},
  issn         = {{1687-689X}},
  language     = {{eng}},
  publisher    = {{Hindawi Limited}},
  series       = {{Physics Research International}},
  title        = {{Microcanonical entropy of the infinite-state potts model}},
  url          = {{http://dx.doi.org/10.1155/2011/437093}},
  doi          = {{10.1155/2011/437093}},
  volume       = {{2011}},
  year         = {{2011}},
}