arXiv subjects

Marcus Benghi Pinto

Publications and source records attributed to Marcus Benghi Pinto.

36 records · Page 2Linked to original sources

arXiv2015

Coexistence of Multiple Phases in Magnetized Quark Matter with Vector Repulsion

We explore the phase structure of dense magnetized quark matter when a repulsive vector interaction, parametrized by $G_V$, is present. Our results show that for a given magnetic field intensity ($B$) one may find a value of $G_V$ for which quark matter may coexist at three different baryonic density values leading to the appearance of two triple points in the phase diagram which have not been observed before. Another novel result is that at high pressure and low temperature we observe a first order transition which presents a negative slope in the $P-T$ that is reminiscent of the solid-liquid transition line observed within the water phase diagram. These unusual patterns occur for $G_V$ and $B$ values which lie within the range presently considered in many investigations related to the study of magnetars.

hep-ph↗

arXiv2014

Dynamical Generation of a Repulsive Vector Contribution to the Quark Pressure

Lattice QCD results for the coefficient $c_2$ appearing in the Taylor expansion of the pressure show that this quantity raises with the temperature towards the Stefan-Boltzmann limit. On the other hand, model approximations predict that when a vector repulsion, parametrized by $G_V$, is present this coefficient reaches a maximum just after $T_c$ and then deviates from the lattice predictions. Recently, this discrepancy has been used as a guide to constrain the (presently unknown) value of $G_V$ within the framework of effective models at large-$N_c$ (LN). In the present investigation we show that, due to finite $N_c$ effects, $c_2$ may also develop a maximum even when $G_V=0$ since a vector repulsive term can be dynamically generated by exchange type of radiative corrections. Here we apply the the Optimized Perturbation Theory (OPT) method to the two flavor Polyakov--Nambu--Jona-Lasinio model (at $G_V=0$) and compare the results with those furnished by lattice simulations an by the LN approximation at $G_V=0$ and also at $G_V \ne 0$. The OPT numerical results for $c_2$ are impressively accurate for $T \lesssim 1.2\, T_c$ but, as expected, predict that this quantity develops a maximum at high-$T$. After identifying the mathematical origin of this extremum we argue that such a discrepant behavior may naturally arise within these effective quark models (at $G_V=0$) whenever the first $1/N_c$ corrections are taken into account. We then interpret this hypothesis as an indication that beyond the large-$N_c$ limit the correct high temperature (perturbative) behavior of $c_2$ will be faithfully described by effective models only if they also mimic the asymptotic freedom phenomenon.

hep-ph↗

arXiv2013

Phase diagram of the magnetized planar Gross-Neveu model beyond the large-N approximation

The phase diagram and thermodynamic properties of the (2+1)-dimensional Gross-Neveu model are studied in the presence of a constant magnetic field. The optimized perturbation theory (OPT) is used to obtain results going beyond the large-N approximation. The free energy and the complete phase diagram of the model, in terms of temperature, chemical potential and magnetic field are obtained and studied in details. By comparing the results from the OPT and the large-N approximation, we conclude that finite N effects favor the phenomenon of inverse magnetic catalysis when the coupling constant is negative. We show that with the OPT the value of the coexistence chemical potential at vanishing temperature always decreases with the magnetic field. This is opposite to what is seen in the large-N approximation, where for large magnetic fields the coexistence chemical potential starts again to increase. Likewise, at finite temperature, the value of the chemical potential at the tricritical point also decreases with the magnetic field in the OPT case. Consequently, the shape of the phase diagrams predicted by the OPT and by the large-N approximation look very different in the presence of high magnetic fields. Finally, for small values of magnetic field and temperature, we identify the presence of possible intermediate nonchiral phase transitions when varying the chemical potential. We show that these phenomena are not an artifact of the large-N approximation and that they also occur within the OPT framework. These intermediate transitions are interpreted to be a consequence of the de Haas--van Alphen oscillations. We also explain why this type of phenomenon can happen in general for negative couplings but not for positive couplings.

hep-ph↗

arXiv2013

Chiral Transition Within Effective Quark Models under Strong Magnetic Fields

In the recently years it has been argued that spectators in heavy ion collisions are responsible for creating a strong magnetic field that could play an important role in the QCD phase transition. In this work we use the SU(2) Nambu--Jona-Lasinio (NJL) model in order to study the chiral transition in quark matter subject to a strong magnetic field. We show some results involving the breaking of chiral symmetry and its restoration at finite temperature and density.

hep-ph↗

arXiv2013

The influence of a repulsive vector coupling in magnetized quark matter

We consider two flavor magnetized quark matter in the presence of a repulsive vector coupling ($G_V$) devoting special attention to the low temperature region of the phase diagram to show how this type of interaction counterbalances the effects produced by a strong magnetic field. The most important effects occur at intermediate and low temperatures affecting the location of the critical end point as well as the region of first order chiral transitions. When $G_V=0$ the presence of high magnetic fields ($eB \ge 10 m_π^2$) increases the density coexistence region with respect to the case when $B$ and $G_V$ are absent while a decrease of this region is observed at high $G_V$ values and vanishing magnetic fields. Another interesting aspect observed at the low temperature region is that the usual decrease of the coexistence chemical value (Inverse Magnetic Catalysis) at $G_V=0$ is highly affected by the presence of the vector interaction which acts in the opposite way. Our investigation also shows that the presence of a repulsive vector interaction enhances the de Haas-van Alphen oscillations which, for very low temperatures, take place at $eB \lesssim 6 m_π^2$. We observe that the presence of a magnetic field, together with a repulsive vector interaction, gives rise to a complex transition pattern since $B$ favors the appearance of multiple solutions to the gap equation whereas $G_V$ turns some metastable solutions into stable ones allowing for a cascade of transitions to occur.

hep-ph↗

arXiv2012

Vector-like contributions from Optimized Perturbation in the Abelian Nambu--Jona-Lasinio model for cold and dense quark matter

Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are obtained with the Optimized Perturbation Theory (OPT) method. These contributions improve the usual mean-field and Hartree-Fock results by generating a $1/N_c$ suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential $μ$, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite $N_c$ contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector-vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For $μ\gtrsim μ_c$ the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree-Fock value $G/(2N_c)$, where $G$ is the scalar coupling, and then increases with $μ$ in a well-determined manner.

nucl-th↗

arXiv2010

Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c

The optimized perturbation theory (OPT) method is applied to the $SU(2)$ version of the Nambu--Jona-Lasinio (NJL) model both at zero and at finite temperature and/or density. At the first nontrivial order the OPT exhibits a class of 1/N_c corrections which produce nonperturbative results that go beyond the standard large-N_c, or mean-field approximation. The consistency of the OPT method with the Goldstone theorem at this order is established, and appropriate OPT values of the basic NJL (vacuum) parameters are obtained by matching the pion mass and decay constant consistently. Deviations from standard large-N_c relations induced by OPT at this order are derived, for example, for the Gell--Mann-Oakes-Renner relation. Next, the results for the critical quantities and the phase diagram of the model, as well as a number of other thermodynamical quantities of interest, are obtained with OPT and then contrasted with the corresponding results at large N_c.

hep-ph↗

arXiv2010

Radiatively Induced Non Linearity in the Walecka Model

We evaluate the effective potential for the conventional linear Walecka non perturbatively up to one loop. This quantity is then renormalized with a prescription which allows finite vacuum contributions to the three as well as four 1PI Green's functions to survive. These terms, which are absent in the standard relativistic Hartree approximation, have a logarithmic energy scale dependence that can be tuned so as to mimic the effects of phi3 and phi4 type of terms present in the non linear Walecka model improving quantities such as the compressibility modulus and the effective nucleon mass, at saturation, by considering energy scales which are very close to the nucleon mass at vanishing density.

nucl-th↗

arXiv2009

Nonperturbative Yukawa theory at finite density and temperature

In-medium Yukawa theory is part of the thermodynamics of the Standard Model of particle physics and is one of the main building blocks of most effective field theories of fermionic systems. By computing its pressure we investigate the nonperturbative thermodynamics at finite temperature and density using the optimized perturbation theory (OPT) framework. Our calculations are valid for arbitrary fermion and scalar masses, temperature, chemical potential, and not restricted to weak coupling. The model is considered in the presence as well as in the absence of condensates. Comparison with nonperturbative results shows that second order perturbation theory (PT) fails in the first case but performs rather well when condensates are absent, even at high-temperature regimes.

hep-ph↗

arXiv2007

Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions

The method of optimized perturbation theory (OPT) is used to study the phase diagram of the massless Gross-Neveu model in 2+1 dimensions. In the temperature and chemical potential plane, our results give strong support to the existence of a tricritical point and line of first order phase transition, previously only suspected to exist from extensive lattice Monte Carlo simulations. In addition of presenting these results we discuss how the OPT can be implemented in conjunction with the Landau expansion in order to determine all the relevant critical quantities.

hep-ph↗

arXiv2007

Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model

A complete thermodynamical analysis of the 2+1 dimensional massless Gross-Neveu model is performed using the optimized perturbation theory. This is a non-perturbative method that allows us to go beyond the known large-N results already at lowest order. Our results, for a finite number of fermion species, N, show the existence of a tricritical point in the temperature and chemical potential phase diagram for discrete chiral phase transition allowing us to precisely to locate it. By studying the phase diagram in the pressure and inverse density plane, we also show the existence of a liquid-gas phase, which, so far, was unknown to exist in this model. Finally, we also derive N dependent analytical expressions for the fermionic mass, critical temperature and critical chemical potential.

hep-th↗

arXiv2007

The 2d Gross-Neveu Model at Finite Temperature and Density with Finite Corrections

We use the linear $δ$ expansion, or optimized perturbation theory, to evaluate the effective potential for the two dimensional Gross-Neveu model at finite temperature and density obtaining analytical equations for the critical temperature, chemical potential and fermionic mass which include finite $N$ corrections. Our results seem to improve over the traditional large-N predictions.

hep-ph↗

arXiv2006

Introducing the notion of bare and effective mass via Newton's second law of motion

The concepts of bare and effective mass are widely used within modern physics. Their meaning is discussed in advanced undergraduate and graduate courses such as solid state physics, nuclear physics and quantum field theory. Here, I discuss how these concepts may be introduced, at a very early stage, together with the discussion of Newton's second law of motion for a sliding block. The setting up of a simple equation for the effective mass will allow instructors to discuss how external parameters, such as the temperature, influence this quantity. By developing the same equation as a power series one may also discuss perturbation theory and introduce Feynman diagrams.

physics.ed-ph↗

arXiv2006

Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N

Using optimized perturbation theory, we evaluate the effective potential for the massless two dimensional Gross-Neveu model at finite temperature and density containing corrections beyond the leading large-N contribution. For large-N, our results exactly reproduce the well known 1/N leading order results for the critical temperature, chemical potential and tricritical points. For finite N, our critical values are smaller than the ones predicted by the large-N approximation and seem to observe Landau's theorem for phase transitions in one space dimension. New analytical results are presented for the tricritical points that include 1/N corrections. The easiness with which the calculations and renormalization are carried out allied to the seemingly convergent optimized results displayed, in this particular application, show the robustness of this method and allows us to obtain neat analytical expressions for the critical as well as tricritical values beyond the results currently known.

hep-th↗

arXiv2006

Effective Potential and Thermodynamics for a Coupled Two-Field Bose Gas Model

We study the thermodynamics of a two-species homogeneous and dilute Bose gas that is self-interacting and quadratically coupled to each other. We make use of field theoretical functional integral techniques and evaluate the one-loop finite temperature effective potential for this system considering the resummation of the leading order temperature dependent as well as infrared contributions. The symmetry breaking pattern associated to the model is then studied by considering different values of self and inter-species couplings. We pay special attention to the eventual appearance of reentrant phases and/or shifts in the observed critical temperatures as compared to the monoatomic (one-field Bose) case.

cond-mat.other↗

arXiv2006

Inverse Symmetry Breaking in Multi-Scalar Field Theories

We review how the phenomena of inverse symmetry breaking (and symmetry nonrestoration) may arise in the context of relativistic as well as nonrelativistic multi-scalar field theories. We discuss how the consideration of thermal effects on the couplings produce different transition patterns for both theories. For the relativistic case, these effects allow the appearance of inverse symmetry breaking (and symmetry nonrestoration) at arbitrarily large temperatures. On the other hand, the same phenomena are suppressed in the nonrelativistic case, which is relevant for condensed matter physics. In this case, symmetry nonrestoration does not happen while inverse symmetry is allowed only to be followed by symmetry restoration characterizing a reentrant phase. The aim of this paper is to give more insight concerning the, qualitatively correct, results obtained by using one loop perturbation theory in the evaluation of thermal masses and couplings.

cond-mat.other↗

arXiv2005

Phase Transitions Patterns in Relativistic and Nonrelativistic Multi-Scalar-Field Models

We discuss the phenomena of symmetry non-restoration and inverse symmetry breaking in the context of multi-scalar field theories at finite temperatures and present its consequences for the relativistic Higgs-Kibble multi-field sector as well as for a nonrelativistic model of hard core spheres. For relativistic scalar field models, it has been shown previously that temperature effects on the couplings do not alter, qualitatively, the phase transition pattern. Here, we show that for the nonrelativistic analogue of these models inverse symmetry breaking, as well as symmetry non-restoration, cannot take place, at high temperatures, when the temperature dependence of the two-body couplings is considered. However, the temperature behavior in the nonrelativistic models allows for the appearance of reentrant phases.

hep-th↗

arXiv2004

Evaluating Critical Exponents in the Optimized Perturbation Theory

We use the optimized perturbation theory, or linear delta expansion, to evaluate the critical exponents in the critical 3d O(N) invariant scalar field model. Regarding the implementation procedure, this is the first successful attempt to use the method in this type of evaluation. We present and discuss all the associated subtleties producing a prescription which can, in principle, be extended to higher orders in a consistent way. Numerically, our approach, taken at the lowest nontrivial order (second order) in the delta expansion produces a modest improvement in comparison to mean field values for the anomalous dimension eta and correlation length nu critical exponents. However, it nevertheless points to the right direction of the values obtained with other methods, like the epsilon-expansion. We discuss the possibilities of improving over our lowest order results and on the convergence to the known values when extending the method to higher orders.

cond-mat.other↗