scholarly journals Phase Structure of Linear Sigma Model without Neutrality Constraint (I)

2012 ◽  
Vol 22 (1) ◽  
pp. 15-31
Author(s):  
Tran Huu Phat ◽  
Nguyen Van Thu
Keyword(s):  
Phase Transition ◽  
Phase Structure ◽  
Sigma Model ◽  
Chiral Limit ◽  
Physical World ◽  
Linear Sigma Model ◽  
Chiral Phase ◽  
Pion Condensation ◽  
First Order Phase Transition ◽  
First Order Phase

The pion condensation and chiral phase transition are studied within the linear sigma model with constituent quarks (LSMq). In the chiral limit the pion condensation is always the first-order phase transition and the phase diagrams of the pion condensate are established respectively in the \((\mu,T) , (\mu_I,T)\) and \((\mu_I,\mu)\)-planes, here \(T, \mu\) and \(\mu_I\) are temperature, baryon chemical and isospin chemical potentials. In the physical world, where the chiral symmetry is explicitly broken we investigate systematically the phase structure of pion and chiral condensates in the \((T-\mu-\mu_I)\)-space. The obtained results are mainly compared to the existing data derived from the lattice QCD (LQCD) and the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model.

Finite-size effects of linear sigma model in compactified space–time

2014 ◽  
Vol 29 (15) ◽  
pp. 1450078 ◽  
Author(s):  
Tran Huu Phat ◽  
Nguyen Van Thu
Keyword(s):  
Phase Transition ◽  
Sigma Model ◽  
Finite Size ◽  
Casimir Energy ◽  
Linear Sigma Model ◽  
Finite Size Effects ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase ◽  
Compactified Space

The finite-sized effect caused by compactified space–time is scrutinized by means of the linear sigma model with constituent quarks at finite temperature T and chemical potential μ, where the compactified spatial dimension with length L is taken along the Oz direction. We find several finite-size effects associated with compactified length L: (a) There are two types of Casimir energy corresponding to two types of quarks, untwisted and twisted quarks. (b) For untwisted quarks, a first-order phase transition emerges at intermediate values of L when the Casimir effect is not taken into account and is enhanced by Casimir energy at small L. (c) For twisted quarks, the phase transition is cross-over everywhere when μ≤200 MeV . When μ> 200 MeV there occurs a first-order phase transition at large L and becomes cross-over at smaller L.

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 Holographic van der Waals Phase Transition for a Hairy Black Hole

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Xiao-Xiong Zeng ◽  
Yi-Wen Han
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Order Phase Transition ◽  
Phase Structure ◽  
Van Der Waals ◽  
Thermal Entropy ◽  
First Order Phase Transition ◽  
Geodesic Length ◽  
First Order Phase ◽  
Hairy Black Hole

The van der Waals (VdW) phase transition in a hairy black hole is investigated by analogizing its charge, temperature, and entropy as the temperature, pressure, and volume in the fluid, respectively. The two-point correlation function (TCF), which is dual to the geodesic length, is employed to probe this phase transition. We find the phase structure in the temperature-thermal entropy plane besides the scale of the horizontal coordinate (geodesic length plane resembles that in the temperature). In addition, we find the equal area law (EAL) for the first-order phase transition and critical exponent of the heat capacity for the second-order phase transition in the temperature-thermal entropy plane (geodesic length plane is consistent with that in temperature), which implies that the TCF is a good probe to probe the phase structure of the back hole.

scholarly journals On the chiral phase transition in the linear sigma model

2004 ◽  
Vol 19 (3) ◽  
pp. 359-365 ◽  
Author(s):  
Tran Huu Phat ◽  
Nguyen Tuan Anh ◽  
Le Viet Hoa
Keyword(s):  
Phase Transition ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Chiral Phase ◽  
Chiral Phase Transition
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