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Fluctuations and thermodynamic geometry of the chiral phase transition
High Energy Physics - Phenomenology · Submitted 7 Oct 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Finally, we find that in the critical region around the critical endpoint $|R|$ scales with the correlation volume, $|R| =K\;\xi^3$, with $K = O(1)$, as expected from hyperscaling; far from the critical endpoint the correspondence between $|R|$ and the correlation volume is not as good as the one we have found at large $\mu$, which is not surprising because at small $\mu$ the chiral crossover is quite smooth; nevertheless, we have found that $R$ develops a characteristic peak structure, suggesting that it is still capable to capture the pseudocritical behavior of the condensate.
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The abstract, sentence by sentence
We study the thermodynamic curvature, $R$, around the chiral phase transition at finite temperature and chemical potential, within the quark-meson model augmented with meson fluctuations. We study the effect of the fluctuations, pions and $\sigma$-meson, on the top of the mean field thermodynamics and how these affect $R$ around the crossover. We find that for small chemical potential the fluctuations enhance the magnitude of $R$, while they do not affect substantially the thermodynamic geometry in the proximity of the critical endpoint. Moreover, in agreement with previous studies we find that $R$ changes sign in the pseudocritical region, suggesting a change of the nature of interactions at the mesoscopic level from statistically repulsive to attractive. Finally, we find that in the critical region around the critical endpoint $|R|$ scales with the correlation volume, $|R| =K\;\xi^3$, with $K = O(1)$, as expected from hyperscaling; far from the critical endpoint the correspondence between $|R|$ and the correlation volume is not as good as the one we have found at large $\mu$, which is not surprising because at small $\mu$ the chiral crossover is quite smooth; nevertheless, we have found that $R$ develops a characteristic peak structure, suggesting that it is still capable to capture the pseudocritical behavior of the condensate.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the thermodynamic curvature, $R$, around the chiral phase transition at finite temperature and chemical potential, within the quark-meson model augmented with meson fluctuations. | contribution 0.96 | 0.94 | 0.04 | asserted 0.85 |
| s1 | We study the effect of the fluctuations, pions and $\sigma$-meson, on the top of the mean field thermodynamics and how these affect $R$ around the crossover. | contribution 0.98 | 0.82 | 0.05 | asserted 0.52 |
| s2 | We find that for small chemical potential the fluctuations enhance the magnitude of $R$, while they do not affect substantially the thermodynamic geometry in the proximity of the critical endpoint. | result 1.00 | 0.97 | 0.33 | asserted 1.00 |
| s3 | Moreover, in agreement with previous studies we find that $R$ changes sign in the pseudocritical region, suggesting a change of the nature of interactions at the mesoscopic level from statistically repulsive to attractive. | result 0.72 | 0.90 | 0.18 | asserted 0.54 |
| s4 | Finally, we find that in the critical region around the critical endpoint $|R|$ scales with the correlation volume, $|R| =K\;\xi^3$, with $K = O(1)$, as expected from hyperscaling; far from the critical endpoint the correspondence between $|R|$ and the correlation volume is not as good as the one we have found at large $\mu$, which is not surprising because at small $\mu$ the chiral crossover is quite smooth; nevertheless, we have found that $R$ develops a characteristic peak structure, suggesting that it is still capable to capture the pseudocritical behavior of the condensate. | result 0.99 | 0.95 | 0.31 | asserted 0.96 |
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The paper
Original abstract
We study the thermodynamic curvature, $R$, around the chiral phase transition at finite temperature and chemical potential, within the quark-meson model augmented with meson fluctuations. We study the effect of the fluctuations, pions and $\sigma$-meson, on the top of the mean field thermodynamics and how these affect $R$ around the crossover. We find that for small chemical potential the fluctuations enhance the magnitude of $R$, while they do not affect substantially the thermodynamic geometry in the proximity of the critical endpoint. Moreover, in agreement with previous studies we find that $R$ changes sign in the pseudocritical region, suggesting a change of the nature of interactions at the mesoscopic level from statistically repulsive to attractive. Finally, we find that in the critical region around the critical endpoint $|R|$ scales with the correlation volume, $|R| =K\;\xi^3$, with $K = O(1)$, as expected from hyperscaling; far from the critical endpoint the correspondence between $|R|$ and the correlation volume is not as good as the one we have found at large $\mu$, which is not surprising because at small $\mu$ the chiral crossover is quite smooth; nevertheless, we have found that $R$ develops a characteristic peak structure, suggesting that it is still capable to capture the pseudocritical behavior of the condensate.
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How the literature uses it
5 arXiv papers cite this in 17 sentences
Papers citing it · 7 sentences without a confident label
Builds on it 1 paper
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We complete the studies of [ref] by analyzing these aspects of $R$ within the FRG approach.
Functional Renormalization Group Study of Thermodynamic Geometry Around the Phase Transition of Quantum Chromodynamic · Introduction · 0.99
Compares with it 1 paper
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Within the mean field approximation, $R$ changes sign around $T_c$, in agreement with previous results [ref] : this was interpreted as the emergence of a boson-like behavior of the system around $T_c$, namely of a statistical attraction in phase space due to long range correlations that develop around $T_c$ that overcomes the statistical fermionic repulsion.
Functional Renormalization Group Study of Thermodynamic Geometry Around the Phase Transition of Quantum Chromodynamic · Results · 0.83
Cites it as background 5 papers
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Within the context of thermodynamic geometry, interesting and recent developments regard its applications to effective models, in particular to the quark-meson (QM) model [ref] .
Functional Renormalization Group Study of Thermodynamic Geometry Around the Phase Transition of Quantum Chromodynamic · Introduction · 0.94
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It has been applied to study the thermodynamics of black holes, in particular thermodynamic instability and phase transitions [ref] .
The Hookean Law of Black Holes and Fragmentation: Insights from Maximum Force Conjecture and Ruppeiner Geometry · Thermodynamic Geometry and the Maximum Force · 0.91
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Other interesting paper can also be found in Refs. [ref] .
The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss-Bonnet gravity: from the critical point to the triple point · Introduction · 0.99
What it cites · 12 sentences without a confident label
Builds on 2 papers
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This study is a natural continuation of previous works [ref] in which the same problem has been analyzed within the mean field approximation.
Thermodynamic Geometry of Nambu -- Jona Lasinio model · Conclusions · 0.98
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This study is a natural continuation of previous works [ref] in which the same problem has been analyzed within the mean field approximation.
Thermodynamic Geometry of the Quark-Meson Model · Conclusions · 0.98
Uses the method or tool of 1 paper
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Being this a first study on fluctuations in the context of thermodynamic curvature, we introduce the fluctuations in the simplest way possible, namely using the Cornwall-Jackiw-Toumbulis (CJT) effective action formalism for composite operators [ref] and limiting ourselves to the largely used Hartree approximation [ref] in which momentum dependent self-energy diagrams are neglected.
Effects of Renormalizing the chiral SU(2) Quark-Meson-Model · Introduction · 1.00
Compares with 2 papers
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We notice that in both cases, $R$ develops a groove around the chiral crossover, in agreement with [ref] .
Thermodynamic Geometry of Nambu -- Jona Lasinio model · The thermodynamic curvature · 0.87
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We notice that in both cases, $R$ develops a groove around the chiral crossover, in agreement with [ref] .
Thermodynamic Geometry of the Quark-Meson Model · The thermodynamic curvature · 0.87
Cites as background 5 papers
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By means of $g_ij$ it is possible to define the scalar curvature, $R$, using the standard definitions of the Riemann geometry; in this context, $R$ is named the thermodynamic curvature, and the theory that studies $R$ is called thermodynamic geometry [ref] .
Thermodynamic Geometry of Nambu -- Jona Lasinio model · Introduction · 0.99
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By means of $g_ij$ it is possible to define the scalar curvature, $R$, using the standard definitions of the Riemann geometry; in this context, $R$ is named the thermodynamic curvature, and the theory that studies $R$ is called thermodynamic geometry [ref] .
Thermodynamic Geometry of the Quark-Meson Model · Introduction · 0.99
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Other fields of application concern Lennard-Jones fluids [ref] , ferromagnetic systems [ref] , gravitational systems and Black Holes [ref] , strong interacting matter [ref] and others [ref] .
Ruppeiner curvature along a renormalization group flow · Thermodynamic geometry · 1.00
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