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A. L. Mota

Publications and source records attributed to A. L. Mota.

At least 19 recordsLinked to original sources
arXiv2024

Tricritical behavior of a relativistic field theory in one dimension

The tricritical behavior in a class of one-dimensional (1D) field theories that exhibit spontaneous symmetry breaking at zero temperature and chemical potential is analyzed. In the Gross-Neveu (GN)-type models of massless fermions the discrete chiral symmetry is spontaneously broken. After doping, the symmetry is restored at a critical chemical potential. We investigate the temperature effects on this doped 1D system under an external constant Zeeman magnetic field $B_0$. We find that $B_0$ suppresses the gapless behavior present for certain values of chemical potential and is able to induce a gapless-gapped phase transition at a critical field strength. We also discuss about the consequences of the consideration of inhomogeneous condensates to the tricritical point, within the Ginzburg-Landau expansion.

hep-th↗
arXiv2024

Correlations equalities and some upper bounds for the coupling constant implying area decay of Wilson loop for $Z_3$ lattice gauge theories

Correlation identities are obtained for $Z_3$ lattice gauge theory where the bonds of the plaquettes are decorated by generalized three-state Ising variables. Making use of correlation inequalities we obtain the area decay of the Wilson loop observable in a range of the coupling parameter larger than those obtained from mean field theory considerations.

hep-lat↗
arXiv2023

The Schwinger and Chiral Schwinger Models in a Non-perturbative Spectral Regularization

We investigate the employment of a non-perturbative regularization scheme -- the spectral regularization, which is based on the gauge technique, previously implemented in the context of chiral quark models -- in the study of the gauge symmetry preservation within the Schwinger model and violation in the chiral Schwinger model. We show that the spectral regularization provides mathematical consistent and ambiguity free solutions for the two-point functions of both Schwinger and chiral Schwinger models in exact (1+1) dimensions, correctly displaying the gauge invariance in the Schwinger model and the axial anomaly in the chiral Schwinger model. The employment of the spectral regularization avoids any dependence on ambiguous amplitudes and/or unconventional $γ^5$ algebra. Our results reinforce the strength of the spectral regularization as a mathematical consistent, divergence free, and ambiguity free regularization scheme that correctly implements symmetry conservation or violation in each case.

hep-th↗
arXiv2020

Finding the Dominant Zero of the Energy Probability Distribution

In this work, we present a method to locate the dominant zero of the Energy Probability Distribution (EPD) Zeros method applied to the study of phase transitions. The technique strongly reduces computer processing time and also increases the accuracy of the results. As an example, we apply it to the 2D Ising model, comparing with both the exact Onsager's results and the previous EPD zeros method results. We show that, for large lattices, the processing time is drastically reduced when compared to other EPD zeros search procedures, whereas for small lattices the gain in accuracy allows very accurate predictions in the thermodynamic limit.

cond-mat.stat-mech↗
arXiv2017

Phase Transition and Monopoles Densities in a Nearest Neighbors Two-Dimensional Spin Ice Model

In this work, we show that, due to the alternating orientation of the spins in the ground state of the artificial square spin ice, the influence of a set of spins at a certain distance of a reference spin decreases faster than the expected result for the long range dipolar interaction, justifying the use of the nearest neighbor two dimensional square spin ice model as an effective model. Using an extension of the model presented in ref. [Scientific Reports 5, 15875 (2015)], considering the influence of the eight nearest neighbors of each spin on the lattice, we analyze the thermodynamics of the model and study the monopoles and string densities dependence as a function of the temperature.

cond-mat.stat-mech↗
arXiv2016

Continuous local model for two-dimensional spin ice

We propose a classical model Hamiltonian with a ground state presenting a spin ice structure. We analyze the introduction of metastable excitations on this ground state, showing the emergence of pairs of magnetic monopoles. The interaction between monopoles and dipoles in the system is studied. As a consequence, we obtain an effective nonlocal interaction between monopoles and dipoles from a local classical spin model.

cond-mat.mtrl-sci↗
arXiv2012

Superfluidity in Two-Dimensional Imbalanced Fermi Gases

We study the zero temperature ground state of a two-dimensional atomic Fermi gas with chemical potential and population imbalance in the mean-field approximation. All calculations are performed in terms of the two-body binding energy $ε_B$, whose variation allows to investigate the evolution from the BEC to the BCS regimes. By means of analytical and exact expressions we show that, similarly to what is found in three dimensions, at fixed chemical potentials, BCS is the ground state until the critical imbalance $h_c$ after which there is a first-order phase transition to the normal state. We find that $h_c$, the Chandrasekhar-Clogston limit of superfluidity, has the same value as in three dimensional systems. We show that for a fixed ratio $ε_B/ε_F$, where $ε_F$ is the two-dimensional Fermi energy, as the density imbalance $m$ is increased from zero, the ground state evolves from BCS to phase separation to the normal state. At the critical imbalance $m_c$ phase separation is not supported and the normal phase is energetically preferable. The BCS-BEC crossover is discussed in balanced and imbalanced configurations. Possible pictures of what may be found experimentally in these systems are also shown. We also investigate the necessary conditions for the existence of bound states in the balanced and imbalanced normal phase.

cond-mat.other↗
arXiv2012

Finite Temperature Phase Diagram of Quasi-Two-Dimensional Imbalanced Fermi Gases Beyond Mean-Field

We investigate the superfluid transition temperature of quasi-two-dimensional imbalanced Fermi gases beyond the mean-field approximation, through the second-order (or induced) interaction effects. For a balanced Fermi system the transition temperature is suppressed by a factor $\approx 2.72$. For imbalanced Fermi systems, the polarization and transition temperature of the tricritical point are significantly reduced as the two-body binding energy $|ε_B|$ increases.

cond-mat.quant-gas↗
arXiv2012

On the coupling constant bounds implying area decay of Wilson loop for Z2 lattice gauge theories with Wilson action Boltzmann factor given by bond variables described by transverse Ising model

We obtain correlation functions for lattice gauge theories with action Boltzmann factor given by bond variables described by transverse Ising model and apply them to obtain area decay of the Wilson loop observable in a range of the coupling parameter larger than that obtained from mean field theory considerations.

cond-mat.stat-mech↗
arXiv2011

Superconductivity in graphene stacks: from the bilayer to graphite

We study the superconducting phase transition, both in a graphene bilayer and in graphite. For that purpose we derive the mean-field effective potential for a stack of graphene layers presenting hopping between adjacent sheets. For describing superconductivity, we assume there is an on-site attractive interaction between electrons and determine the superconducting critical temperature as a function of the chemical potential. This displays a dome-shaped curve, in agreement with previous results for two-dimensional Dirac fermions. We show that the hopping between adjacent layers increases the critical temperature for small values of the chemical potential. Finally, we consider a minimal model for graphite and show that the transition temperature is higher than that for the graphene bilayer for small values of chemical potential. This might explain why intrinsic superconductivity is observed in graphite.

cond-mat.supr-con↗
arXiv2009

Momentum Space Regularizations and the Indeterminacy in the Schwinger Model

We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an {\it ansatz} in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and their violations are discussed. The analysis is carried out in both analytical and sharp cutoff regularization procedures. We also show how the Pauli Villars regularization scheme eliminates the indeterminacy, giving a gauge invariant result in the vector Schwinger model.

hep-th↗
arXiv2009

Axial Vector Coupling and Chiral Anomaly in the Spectral Quark Model

We studied the Adler-Bardeen-Bell-Jackiw anomaly in the context of a finite chiral quark model known as the Spectral Quark Model. Within this model, we obtain the general non-local form of the axial vertex compatible with a non vanishing axial coupling, in the chiral limit. The triangle anomaly is computed and we show that the obtained dependence of the axial vertex with the spectral mass is necessary to ensure both finiteness and the correct violation of the chiral Ward-Takahashi identity.

hep-th↗
arXiv2008

Temperature Effects in a Fermi Gas with Population Imbalance

We investigate temperature effects in a Fermi gas with imbalanced spin populations. From the general expression of the thermal gap equation we find, in {\it weak coupling limit}, an analytical expression for the transition temperature $T_c$ as a function of various possibilities of chemical potential and mass asymmetries between the two particle species. For a range of asymmetry between certain specific values, this equation always has two solutions for $T_c$ which has been interpreted as a reentrant phenomena or a pairing induced by temperature effect. We show that the lower $T_c$ is never related to a stable solution. The same results are obtained in {\it strong coupling limit}. The thermodynamical potential is carefully analyzed to avoid the consideration of the unstable solutions. We also obtain the tricritical points for the chemical potential and mass imbalanced cases, and beyond these points we properly minimize the thermodynamic potential to find the stable and metastable first order transition lines.

cond-mat.str-el↗
arXiv2006

Relativistic NJL Model with Light and Heavy Quarks

We study the Nambu-Jona-Lasinio model with light and heavy quarks in a relativistic approach. We emphasize relevant regularization issues as well as the transition from light to heavy quarks. The approach of the electromagnetic meson form factor to the Isgur-Wise function in the heavy quark limit is also discussed.

hep-ph↗
arXiv2006

The Role of hidden ambiguities in the Linear Sigma Model with fermions

The $U_L(3)\times U_R(3)$ Linear Sigma Model (LSM) with quark degrees of freedom is used to show that radiative corrections generate undetermined finite contributions. Their origin is related to surface terms which are differences between divergent integrals with the same degree of divergence. The technique used to detect these ambiguities is an implicit regularization on basic divergent integrals that do not depend on external momenta. We show that such contributions are absorbed by renormalization or fixed by symmetry requirements. The general expression for surface terms is derived. Renormalization group coefficients are calculated, as well as relevant observables for this model, such as $f_π$, $f_k$ and the pion and kaon form factors.

hep-ph↗
arXiv2005

Symmetries and Ambiguities in the linear sigma model with light quarks

We investigate the role of undetermined finite contributions generated by radiative corrections in a $SU(2)\times SU(2)$ linear sigma model with quarks. Although some of such terms can be absorbed in the renormalization procedure, one such contribution is left in the expression for the pion decay constant. This arbitrariness is eliminated by chiral symmetry.

hep-ph↗