Narrow Results

The spin-1 Ising (BEG) model has been simulated on a cellular automaton improved from the Creutz cellular automaton (CCA) for a face-centered cubic lattice. The simulations have been made in the 0 ≤ d = D/J ≤ 7 and -1.25 < k = K/J ≤ 0 parameter region. In this region, the ground state diagram (k, d) has ferromagnetic and perfect zero ordering regions. The ferromagnetic ordering region separates into four regions which exhibit different phase transition types as the first order, the second order, the reentrant, the double-reentrant and the successive phase transitions. The simulation results show that the model has the tricritical points, the critical end points and the bicritical points on the (kT_C/zJ, d) and (kT_C/zJ, k) planes as indicated by the Mean Field approximation results.

This paper is devoted to locate the position of critical end point (CEP) and study its properties. The CEP for different current quark masses are located. It is found that as the current quark mass tends to zero, the position of the CEP tends to the tricrtical point (TCP), while the height of the chiral susceptibility tends to infinity faster and faster, which indicates that the transition from CEP to TCP is continuous. This continuity causes the so-called hidden TCP effect.

Three representations of Nambu–Jona-Lasinio interaction Lagrangians are constructed by Fierz transformation, and gap equation and critical end point in these three representations at finite temperature and finite chemical potential are studied. We find that the values of the quark mass and the critical end point are different in these three representations because of the consideration of Hartree–Fock approximation in our calculation.

In this paper, chiral chemical potential ${\mu }_5$ is introduced to investigate the QCD susceptibilities and chiral phase transition within the Polyakov-loop-extended Nambu–Jona-Lasinio models in the mean-field approximation. We concentrate on the effect of chiral chemical potential on the phase diagram and the QCD susceptibilities. Moreover, it is worth noting that chiral chemical potential has more and more prominent impact on the susceptibilities and the phase diagram with the decrease of temperature based on our results, which coincides with the prediction that the chiral symmetry is dynamically broken in the first-order phase transition region and gets partly restored in the crossover region.

In the mean field approximation of (2 + 1)-flavor Nambu–Jona-Lasinio model, we strictly derive several sets of coupled equations for the chiral susceptibility, the quark number susceptibility, etc. at finite temperature and quark chemical potential. The critical exponents of these susceptibilities in the vicinity of the QCD critical end point (CEP) are presented in SU(2) and SU(3) cases, respectively. It is found that these various susceptibilities share almost the same critical behavior near the CEP. The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included.

We use the linear sigma model coupled to quarks, together with a plausible location of the critical end point (CEP), to study the chiral symmetry transition in the QCD phase diagram. We compute the effective potential at finite temperature and density up to the contribution of the ring diagrams, both in the low and high temperature limits, and use it to compute the pressure and the position of the CEP. In the high temperature regime, by comparing to results from extrapolated lattice data, we determine the model coupling constants. Demanding that the CEP remains in the same location when described in the high temperature limit, we determine again the couplings and the pressure for the low temperature regime. We show that this procedure gives an average description of the lattice QCD results for the pressure and that the change from the low to the high temperature domains in this quantity can be attributed to the change in the coupling constants which in turn we link to the change in the effective degrees of freedom.

In this paper, we explore the critical end point in the $T-\mu$ phase diagram of a thermomagnetic nonlocal Nambu–Jona-Lasinio model in the weak field limit. We work with the Gaussian regulator, and find that a crossover takes place at $\mu$, $B=0$. The crossover turns to a first-order phase transition as the chemical potential or the magnetic field increases. The critical end point of the phase diagram occurs at a higher temperature and lower chemical potential as the magnetic field increases. This result is in accordance to similar findings in other effective models. We also find that there is a critical magnetic field, for which a first-order phase transition takes place even at $\mu =0$.