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Register a new userFinite Size Effects on the Chiral Phase Transition of Quantum Chromodynamics
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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, $mu$. 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 {it 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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The nuclear force acting between protons and neutrons is studied in the Monte Carlo simulations of the fundamental theory of the strong interaction, the quantum chromodynamics defined on the hypercubic space-time lattice. After a brief summary of the empirical nucleon-nucleon (NN) potentials which can fit the NN scattering experiments in high precision, we outline the basic formulation to derive the potential between the extended objects such as the nucleons composed of quarks. The equal-time Bethe-Salpeter amplitude is a key ingredient for defining the NN potential on the lattice. We show the results of the numerical simulations on a $32^4$ lattice with the lattice spacing $a simeq 0.137 $fm (lattice volume (4.4 fm)$^4$) in the quenched approximation. The calculation was carried out using the massively parallel computer Blue Gene/L at KEK. We found that the calculated NN potential at low energy has basic features expected from the empirical NN potentials; attraction at long and medium distances and the repulsive core at short distance. Various future directions along this line of research are also summarized.
The properties of two-flavored massless Nambu-Jona-Lasinio model in (1+1)-dimensional $R^1times S^1$ spacetime with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials $mu_I$, $mu$. The consideration is performed in the large $N_c$ limit, where $N_c$ is the number of colored quarks. It is shown that at $L=infty$ ($L$ is the length of the circumference $S^1$) the pion condensation (PC) phase with {it zero quark number density} is realized at arbitrary nonzero $mu_I$ and for rather small values of $mu$. However, at arbitrary finite values of $L$ the phase portrait of the model contains the PC phase with {it nonzero quark number density} (in the case of periodic boundary conditions for quark fields). Hence, finite sizes of the system can serve as a factor promoting the appearance of the PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of $L$.
We study the dressing of four-quark interaction by the ring diagram in an effective chiral quark model. Implementing such an in-medium coupling naturally reduces the chiral transition temperature in a class of chiral models, and is capable of generating the inverse magnetic catalysis at finite temperatures. We also demonstrate the important role of confining forces, via the Polyakov loop, in a positive feedback mechanism which reinforces the inverse magnetic catalysis.
We consider a model of chiral phase transitions in nuclei, suggested by T.D. Lee et al., and argue that such transitions may be seen in cumulative effect investigations. Finite-range effects arising from the smallness of the system are briefly discussed. Some general proposals for future NICA and CBM experiments are given.
While it is known that the QCD vacuum in a magnetic background exhibits both diamagnetic and paramagnetic characteristics in the low-energy domain, a systematic investigation of the corresponding phases emerging in the pion-dominated regime is still lacking. Here, within two-flavor chiral perturbation theory, taking into account the pion-pion interaction, we analyze the subtle interplay between zero- and finite-temperature portions in the magnetization and magnetic susceptibility. The dependence of the magnetic susceptibility on temperature and magnetic field strength in the paramagnetic and diamagnetic phase is non-monotonic. Our low-energy analysis complements lattice QCD that is currently operating at higher temperatures and stronger magnetic fields.
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