Thermodynamic geometry of Nambu–Jona Lasinio model

Castorina, P.; Lanteri, D.; Mancani, Salvo

doi:10.1140/epjp/s13360-019-00004-3

Cited by 7 publications

(15 citation statements)

References 42 publications

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“…The curvature is found to be positive at low temperature, as for an ideal fermion gas; then a change of sign is observed near the chiral crossover, where R develops a local minimum which becomes more pronounced when the chemical potential is increased; finally, R becomes positive again at high temperature and approaches zero from above. A change of sign of R has been observed for many substances [18,20,22,23,25,[27][28][29]31] as well as in previous studied on the thermodynamic curvature of the chiral phase transition [43,44] and it has been interpreted in terms of the nature of the attractive/repulsive microscopic interaction. We support this idea here, and we interpret the change of sign of R around the chiral crossover as a rearrangement of the interaction at a mesoscopic level, from statistically repulsive far from the crossover to attractive around the crossover.…”

Section: Introductionmentioning

confidence: 59%

Fluctuations and thermodynamic geometry of the chiral phase transition

Castorina,

Lanteri,

Ruggieri

2020

Preprint

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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 σ−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 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| = Kξ 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 µ, which is not surprising because at small µ 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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Section: Introductionmentioning

confidence: 59%

Fluctuations and thermodynamic geometry of the chiral phase transition

Castorina,

Lanteri,

Ruggieri

2020

Preprint

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“…The inclusion of the Polyakov loop to take trace of confinementdeconfinement phase transition via a collective field would also be possible [42][43][44]. Finally, it is of a certain interest to analyze the thermodynamic geometry [31,[45][46][47][48][49][50][51][52][53][54] of the effective models of chiral symmetry breaking with finite size. We plan to report on these topics in the near future.…”

Section: Discussionmentioning

confidence: 99%

Finite Size Effects on the Chiral Phase Transition of Quantum Chromodynamics

Wan,

Li,

Zhang

et al. 2020

Preprint

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We study the effect of periodic boundary conditions on chiral symmetry breaking and its restoration in Quantum Chromodynamics. As an effective model of the effective potential for the quark condensate, we use the quark-meson model, while the theory is quantized in a cubic box of size L. After specifying a renormalization prescription for the vacuum quark loop, we study the condensate at finite temperature, T , and quark chemical potential, µ. We find that lowering L leads to a catalysis of chiral symmetry breaking. The excitation of the zero mode leads to a jump in the condensate at low temperature and high density, that we suggest to interpret as a gas-liquid phase transition that takes place between the chiral symmetry broken phase (hadron gas) and chiral symmetry restored phase (quark matter). We characterize this intermediate phase in terms of the increase of the baryon density, and of the correlation length of the fluctuations of the order parameter: for small enough L the correlation domains occupy a substantial portion of the volume of the system, and the fluctuations are comparable to those in the critical region. For these reasons, we dub this phase as the subcritical liquid. The qualitative picture that we draw is in agreement with previous studies based on similar effective models. We also clarify the discrepancy on the behavior of the critical temperature versus L found in different models.

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“…On the other hand, for AdS BHs, R TG always points to attractive interaction. Although, in other systems, changes of sign of R TG have been seen [23][24][25] near the critical point (and, although recent general results, on the fundamental quantum gravitational interaction, indicate a fermionic nature of such degrees of freedom [72]), we take here the view that the physical region for Schwarzschild BHs in conformal gravity requires an entropy greater than the S 0 in Eq. (69), in order to have a consistent interpretation with the attractive nature of the gravitational interaction.…”

Section: Stability Analysis: Specific Heat and Tgmentioning

confidence: 96%

“…This way, critical phenomena are related to distinctive signs of the scalar curvature, R TG , obtained from such metric: R TG = 0 means a system made of noninteracting components, while for R TG < 0 such components attract each other, and for R TG > 0 repel each other. Moreover, R TG diverges in a second order phase transition as the correlation volume, while it appears to have a local maximum at a crossover, as happens in quantum chromodynamics [23][24][25][26][27]. TG has been tested in many different systems: phase coexistence for helium, hydrogen, neon and argon [28], for the Lennard Jones fluids [29,30], for ferromagnetic systems and liquid liquid phase transitions [31]; in the liquid gas like first order phase transition in dyonic charged AdS BH [32]; in quantum chromodynamics (QCD) to describe crossover from Hadron gas and Quark Gluon Plasma [23][24][25][26][27]; in the Hawking Page transitions in Gauss Bonnet AdS [33], Reissner Nordstrom AdS and the Kerr AdS [34].…”

Section: Introductionmentioning

confidence: 92%

“…Moreover, R TG diverges in a second order phase transition as the correlation volume, while it appears to have a local maximum at a crossover, as happens in quantum chromodynamics [23][24][25][26][27]. TG has been tested in many different systems: phase coexistence for helium, hydrogen, neon and argon [28], for the Lennard Jones fluids [29,30], for ferromagnetic systems and liquid liquid phase transitions [31]; in the liquid gas like first order phase transition in dyonic charged AdS BH [32]; in quantum chromodynamics (QCD) to describe crossover from Hadron gas and Quark Gluon Plasma [23][24][25][26][27]; in the Hawking Page transitions in Gauss Bonnet AdS [33], Reissner Nordstrom AdS and the Kerr AdS [34]. A list of results have been obtained by applying TG to BHs [35][36][37][38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 92%

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Stability of Schwarzschild (Anti)de Sitter black holes in conformal gravity

et al. 2021

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We study the thermodynamics of spherically symmetric, neutral and non-rotating black holes in conformal (Weyl) gravity. To this end, we apply different methods: (i) the evaluation of the specific heat; (ii) the study of the entropy concavity; (iii) the geometrical approach to thermodynamics known as thermodynamic geometry; (iv) the Poincaré method that relates equilibrium and out-of-equilibrium thermodynamics. We show that the thermodynamic geometry approach can be applied to conformal gravity too, because all the key thermodynamic variables are insensitive to Weyl scaling. The first two methods, (i) and (ii), indicate that the entropy of a de Sitter black hole is always in the interval $$2/3\le S\le 1$$ 2 / 3 ≤ S ≤ 1 , whereas thermodynamic geometry suggests that, at $$S=1$$ S = 1 , there is a second order phase transition to an Anti de Sitter black hole. On the other hand, we obtain from the Poincaré method (iv) that black holes whose entropy is $$S < 4/3$$ S < 4 / 3 are stable or in a saddle-point, whereas when $$S>4/3$$ S > 4 / 3 they are always unstable, hence there is no definite answer on whether such transition occurs. Since thermodynamics geometry takes the view that the entropy is an extensive quantity, while the Poincaré method does not require extensiveness, it is valuable to present here the analysis based on both approaches, and so we do.

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Thermodynamic geometry of Nambu–Jona Lasinio model

Cited by 7 publications

References 42 publications

Fluctuations and thermodynamic geometry of the chiral phase transition

Fluctuations and thermodynamic geometry of the chiral phase transition

Finite Size Effects on the Chiral Phase Transition of Quantum Chromodynamics

Stability of Schwarzschild (Anti)de Sitter black holes in conformal gravity

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