Phase transitions in the complex plane of physical parameters
At low temperature, a thermodynamic system undergoes a phase transition when a physical parameter passes through a singularity point of the free energy. This corresponds to the formation of a new order. At high temperature, thermal fluctuations destroy the order. Correspondingly, the free energy is...
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Nature Publishing Group
2014
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4047537/ |
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pubmed-40475372014-06-12 Phase transitions in the complex plane of physical parameters Wei, Bo-Bo Chen, Shao-Wen Po, Hoi-Chun Liu, Ren-Bao Article At low temperature, a thermodynamic system undergoes a phase transition when a physical parameter passes through a singularity point of the free energy. This corresponds to the formation of a new order. At high temperature, thermal fluctuations destroy the order. Correspondingly, the free energy is a smooth function of the physical parameter and singularities only occur at complex values of the parameter. Since a complex valued parameter is unphysical, no phase transitions are expected when the physical parameter is varied. Here we show that the quantum evolution of a system, initially in thermal equilibrium and driven by a designed interaction, is equivalent to the partition function of a complex parameter. Therefore, we can access the complex singularity points of thermodynamic functions and observe phase transitions even at high temperature. We further show that such phase transitions in the complex plane are related to topological properties of the renormalization group flows of the complex parameters. This result makes it possible to study thermodynamics in the complex plane of physical parameters. Nature Publishing Group 2014-06-06 /pmc/articles/PMC4047537/ /pubmed/24902497 http://dx.doi.org/10.1038/srep05202 Text en Copyright © 2014, Macmillan Publishers Limited. All rights reserved http://creativecommons.org/licenses/by-nc-sa/3.0/ This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. The images in this article are included in the article's Creative Commons license, unless indicated otherwise in the image credit; if the image is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the image. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ |
| repository_type |
Open Access Journal |
| institution_category |
Foreign Institution |
| institution |
US National Center for Biotechnology Information |
| building |
NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Wei, Bo-Bo Chen, Shao-Wen Po, Hoi-Chun Liu, Ren-Bao |
| spellingShingle |
Wei, Bo-Bo Chen, Shao-Wen Po, Hoi-Chun Liu, Ren-Bao Phase transitions in the complex plane of physical parameters |
| author_facet |
Wei, Bo-Bo Chen, Shao-Wen Po, Hoi-Chun Liu, Ren-Bao |
| author_sort |
Wei, Bo-Bo |
| title |
Phase transitions in the complex plane of physical parameters |
| title_short |
Phase transitions in the complex plane of physical parameters |
| title_full |
Phase transitions in the complex plane of physical parameters |
| title_fullStr |
Phase transitions in the complex plane of physical parameters |
| title_full_unstemmed |
Phase transitions in the complex plane of physical parameters |
| title_sort |
phase transitions in the complex plane of physical parameters |
| description |
At low temperature, a thermodynamic system undergoes a phase transition when a physical parameter passes through a singularity point of the free energy. This corresponds to the formation of a new order. At high temperature, thermal fluctuations destroy the order. Correspondingly, the free energy is a smooth function of the physical parameter and singularities only occur at complex values of the parameter. Since a complex valued parameter is unphysical, no phase transitions are expected when the physical parameter is varied. Here we show that the quantum evolution of a system, initially in thermal equilibrium and driven by a designed interaction, is equivalent to the partition function of a complex parameter. Therefore, we can access the complex singularity points of thermodynamic functions and observe phase transitions even at high temperature. We further show that such phase transitions in the complex plane are related to topological properties of the renormalization group flows of the complex parameters. This result makes it possible to study thermodynamics in the complex plane of physical parameters. |
| publisher |
Nature Publishing Group |
| publishDate |
2014 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4047537/ |
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1612097670853165056 |