Chiral logarithmic sigma model at finite temperature and baryonic chemical potential

2014 ◽  
Vol 29 (34) ◽  
pp. 1450176 ◽  
Author(s):  
M. Abu-Shady
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Sigma Model ◽  
Present Model ◽  
Chemical Potential ◽  
Logarithmic Potential ◽  
Chiral Phase ◽  
Baryonic Chemical Potential ◽  
Breaking Symmetry ◽  
Good Agreement

A logarithmic potential is suggested to study the chiral phase transition, the critical temperature, and the meson masses at finite temperature and baryonic chemical potential. The logarithmic potential is based on some aspects of quantum chromodynamics (QCD) theory. The model has been solved in the mean-field approximation. We found that the behavior of meson masses takes a similar behavior as in the original sigma model and the Nambu–Jona-Lasinio model. The critical temperature is reduced in comparison with the original sigma model and it is in good agreement with recent lattice QCD results. The chiral phase transition is crossover in the case of chiral explicit breaking symmetry. The Goldstone boson theorem is studied, in which the meson mass is massive and pion mass is massless at lower temperatures. Our conclusions indicate to the present model successfully predicts the phase transition as well as in the original quark sigma model and the Nambu–Jona–Lasinio model. A new advantage of the present model, the critical temperature is in good agreement with lattice QCD results at zero chemical potential. A condition of spontaneous breaking symmetry is necessary to satisfy the Goldstone theorem in the chiral limit.

PHASE TRANSITION PATTERNS OF NUCLEAR MATTER BASED ON EXTENDED LINEAR SIGMA MODEL

2013 ◽  
Vol 22 (11) ◽  
pp. 1350077 ◽  
Author(s):  
TRAN HUU PHAT ◽  
NGUYEN TUAN ANH ◽  
PHUNG THI THU HA
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Nuclear Matter ◽  
Degrees Of Freedom ◽  
Sigma Model ◽  
Chemical Potential ◽  
Linear Sigma Model ◽  
Baryon Chemical Potential ◽  
Chiral Phase ◽  
The Relationship

We study systematically various types of phase transitions in nuclear matter at finite temperature T and baryon chemical potential μ based on the extended linear sigma model with nucleon degrees of freedom. It is shown that there are three types of phase transitions in nuclear matter: the chiral symmetry nonrestoration (SNR) at high temperature, the well-known liquid–gas (LG) phase transition at sub-saturation density and the Lifshitz phase transition (LPT) from the fully-gapped state to the state with Fermi surface. Their phase diagrams are established in the (T, μ)-plane and their physical properties are investigated in detail. The relationship between the chiral phase transition and the LG phase transition in nuclear matter is discussed.

scholarly journals Chiral Phase Transition in Linear Sigma Model with Nonextensive Statistical Mechanics

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Ke-Ming Shen ◽  
Hui Zhang ◽  
De-Fu Hou ◽  
Ben-Wei Zhang ◽  
En-Ke Wang
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Statistical Mechanics ◽  
Sigma Model ◽  
Chemical Potential ◽  
Linear Sigma Model ◽  
Nonextensive Statistical Mechanics ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Lower Temperature

From the nonextensive statistical mechanics, we investigate the chiral phase transition at finite temperature T and baryon chemical potential μB in the framework of the linear sigma model. The corresponding nonextensive distribution, based on Tsallis’ statistics, is characterized by a dimensionless nonextensive parameter, q, and the results in the usual Boltzmann-Gibbs case are recovered when q→1. The thermodynamics of the linear sigma model and its corresponding phase diagram are analysed. At high temperature region, the critical temperature Tc is shown to decrease with increasing q from the phase diagram in the (T,μ) plane. However, larger values of q cause the rise of Tc at low temperature but high chemical potential. Moreover, it is found that μ different from zero corresponds to a first-order phase transition while μ=0 to a crossover one. The critical endpoint (CEP) carries higher chemical potential but lower temperature with q increasing due to the nonextensive effects.

scholarly journals Linear Sigma Model at Finite Temperature and Baryonic Chemical Potential Using the N-Midpoint Technique

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
M. Abu-Shady
Keyword(s):  
Energy Density ◽  
Thermodynamic Properties ◽  
Effective Potential ◽  
Finite Temperature ◽  
Sigma Model ◽  
Chemical Potential ◽  
Linear Sigma Model ◽  
Midpoint Rule ◽  
Baryonic Chemical Potential ◽  
Good Agreement

A baryonic chemical potential (μb) is included in the linear sigma model at finite temperature. The effective mesonic potential is numerically calculated using the N-midpoint rule. The meson masses are investigated as functions of the temperature (T) at fixed value of baryonic chemical potential. The pressure and energy density are investigated as functions of temperature at fi…xed value of μb. The obtained results are in good agreement in comparison with other techniques. We conclude that the calculated effective potential successfully predicts the meson properties and thermodynamic properties at finite baryonic chemical potential.

scholarly journals Using the Linear Sigma Model with quarks to describe the QCD phase diagram and to locate the critical end point

2018 ◽  
Vol 172 ◽  
pp. 08002
Author(s):  
Alejandro Ayala ◽  
Jorge David Castaño-Yepes ◽  
José Antonio Flores ◽  
Saúl Hernández ◽  
Luis Hernández
Keyword(s):  
Phase Diagram ◽  
Critical Temperature ◽  
Sigma Model ◽  
Chemical Potential ◽  
Linear Sigma Model ◽  
Transition Line ◽  
Baryon Chemical Potential ◽  
First Order ◽  
Qcd Phase Diagram ◽  
Crossover Transition

We study the QCD phase diagram using the linear sigma model coupled to quarks. We compute the effective potential at finite temperature and quark chemical potential up to ring diagrams contribution. We show that, provided the values for the pseudo-critical temperature Tc = 155 MeV and critical baryon chemical potential μBc ≃ 1 GeV, together with the vacuum sigma and pion masses. The model couplings can be fixed and that these in turn help to locate the region where the crossover transition line becomes first order.

Studies on proper time regularization and the QCD chiral phase transition

2019 ◽  
Vol 34 (01) ◽  
pp. 1950003
Author(s):  
Yu-Qiang Cui ◽  
Zhong-Liang Pan
Keyword(s):  
Phase Transition ◽  
Small Parameter ◽  
Effective Mass ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Proper Time ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Njl Model ◽  
The Difference

We investigate the finite-temperature and zero quark chemical potential QCD chiral phase transition of strongly interacting matter within the two-flavor Nambu–Jona-Lasinio (NJL) model as well as the proper time regularization. We use two different regularization processes, as discussed in Refs. 36 and 37, separately, to discuss how the effective mass M varies with the temperature T. Based on the calculation, we find that the M of both regularization schemes decreases when T increases. However, for three different parameter sets, quite different behaviors will show up. The results obtained by the method in Ref. 36 are very close to each other, but those in Ref. 37 are getting farther and farther from each other. This means that although the method in Ref. 37 seems physically more reasonable, it loses the advantage in Ref. 36 of a small parameter dependence. In addition, we also, find that two regularization schemes provide similar results when T [Formula: see text] 100 MeV, while when T is larger than 100 MeV, the difference becomes obvious: the M calculated by the method in Ref. 36 decreases more rapidly than that in Ref. 37.

scholarly journals Holographic s-wave superconductors with Horndeski correction

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Jun-Wang Lu ◽  
Ya-Bo Wu ◽  
Li-Gong Mi ◽  
Hao Liao ◽  
Bao-Ping Dong
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Critical Temperature ◽  
Chemical Potential ◽  
Low Frequency ◽  
S Wave ◽  
Quasiparticle Excitation ◽  
Numerical Result ◽  
Ads Black Holes ◽  
Numerical And Analytical Methods

Abstract Via both numerical and analytical methods, we build the holographic s-wave insulator/superconductor model in the five-dimensional AdS soliton with the Horndeski correction in the probe limit and study the effects of Horndeski parameter k on the superconductor model. For the fixed mass squared of the scalar field ($$m^2$$m2), the critical chemical potential $$\mu _c$$μc increases with the larger Horndeski parameter k, which means that the increasing Horndeski correction hinders the superconductor phase transition. Meanwhile, above the critical chemical potential, the obvious pole arises in the low frequency of the imaginal part of conductivity, which signs the appearance of superconducting state. What is more, the energy of quasiparticle excitation decreases with the larger Horndeski correction. Furthermore, the critical exponent of the condensate (charge density) is $$\frac{1}{2}$$12 (1), which is independent of the Horndeski correction. In addition, the analytical results agree well with the numerical results. Subsequently, the conductor/superconductor model with Horndeski correction is analytically realized in the four- and five-dimensional AdS black holes. It is observed that the increasing Horndeski correction decreases the critical temperature and thus hinders the superconductor phase transition, which agrees with the numerical result in the previous works.

scholarly journals Construction of a Universal Gel Model with Volume Phase Transition

Gels ◽  
2020 ◽  
Vol 6 (1) ◽  
pp. 7
Author(s):  
Gerald S. Manning
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Equation Of State ◽  
Chemical Potential ◽  
Van Der Waals ◽  
Density Fluctuations ◽  
Volume Phase Transition ◽  
Restoring Force ◽  
Intrinsic Volume ◽  
Volume Phase

The physical principle underlying the familiar condensation transition from vapor to liquid is the competition between the energetic tendency to condense owing to attractive forces among molecules of the fluid and the entropic tendency to disperse toward the maximum volume available as limited only by the walls of the container. Van der Waals incorporated this principle into his equation of state and was thus able to explain the discontinuous nature of condensation as the result of instability of intermediate states. The volume phase transition of gels, also discontinuous in its sharpest manifestation, can be understood similarly, as a competition between net free energy attraction of polymer segments and purely entropic dissolution into a maximum allowed volume. Viewed in this way, the gel phase transition would require nothing more to describe it than van der Waals’ original equation of state (with osmotic pressure Π replacing pressure P). But the polymer segments in a gel are networked by cross-links, and a consequent restoring force prevents complete dissolution. Like a solid material, and unlike a van der Waals fluid, a fully swollen gel possesses an intrinsic volume of its own. Although all thermodynamic descriptions of gel behavior contain an elastic component, frequently in the form of Flory-style rubber theory, the resulting isotherms usually have the same general appearance as van der Waals isotherms for fluids, so it is not clear whether the solid-like aspect of gels, that is, their intrinsic volume and shape, adds any fundamental physics to the volume phase transition of gels beyond what van der Waals already knew. To address this question, we have constructed a universal chemical potential for gels that captures the volume transition while containing no quantities specific to any particular gel. In this sense, it is analogous to the van der Waals theory of fluids in its universal form, but although it incorporates the van der Waals universal equation of state, it also contains a network elasticity component, not based on Flory theory but instead on a nonlinear Langevin model, that restricts the radius of a fully swollen spherical gel to a solid-like finite universal value of unity, transitioning to a value less than unity when the gel collapses. A new family of isotherms arises, not present in a preponderately van der Waals analysis, namely, profiles of gel density as a function of location in the gel. There is an abrupt onset of large amplitude density fluctuations in the gel at a critical temperature. Then, at a second critical temperature, the entire swollen gel collapses to a high-density phase.

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