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B. V. Costa

Publications and source records attributed to B. V. Costa.

At least 19 recordsLinked to original sources
arXiv2024

Connecting the Unstable Region of the Entropy to the Pattern of the Fisher's Zeros Map

Phase transitions are one of the most interesting natural phenomena. For finite systems, one of the concerns in the topic is how to classify a specific transition as being of first, second, or even of a higher order, according to the Ehrenfest classification. The partition function provides all the thermodynamic information about the physical systems, and a phase transition can be identified by the complex temperature where it is equal to zero. In addition, the pattern of the zeros on the complex temperature plane can provide evidence of the order of the transition. In this manuscript, we present an analytical and simulational study connecting the microcanonical analysis of the unstable region of the entropy to the canonical partition function zeros. We show that, for the first-order transition, the zeros accumulate uniformly in a vertical line on the complex inverse temperature plane as discussed in previous works. We illustrate our calculation using the $147$ particles Lennard-Jones cluster.

cond-mat.stat-mech↗
arXiv2022

Phase Diagram of Flexible Polymers with Quenched Disordered Charged Monomers

Recent advances in Generalized Ensemble simulations and microcanonical analysis allowed the investigation of structural transitions in polymer models over a broad range of local bending and torsion strengths. It is reasonable to argue that electrostatic interactions play a significant role in stabilizing and mediating structural transitions in polymers. We propose a bead-spring polymer model with randomly distributed charged monomers interacting via a screened Coulomb potential. By combining the Replica Exchange Wang-Landau (REWL) method with energy-dependent monomer updates, we constructed the hyperphase diagram as a function of temperature ($T$) and charged monomer concentration ($η$). The coil-globule and globular-solid transitions are respectively second and first order for the entire concentration range. However, above a concentration threshold of $η=80\%$, electrostatic repulsion hinders the formation of solid and liquid globules, and the interplay between enthalpic and entropic interactions leads to the formation of liquid pearl-necklace ad solid helical structures. The probability distribution, $P(E,T)$, indicates that at high $η$, the pearl-necklace liquid phase freezes into a stable solid helix-like structure with a free energy barrier higher than the freezing globule transition at low $η$.

cond-mat.soft↗
arXiv2021

Pushing the limits of EPD zeros method

The use of partition function zeros in the study of phase transition is growing in the last decade mainly due to improved numerical methods as well as novel formulations and analysis. In this paper the impact of different parameters choice for the energy probability distribution (EPD) zeros recently introduced by Costa et al is explored in search for optimal values. Our results indicate that the EPD method is very robust against parameter variations and only small deviations on estimated critical temperatures are found even for large variation of parameters, allowing to obtain accurate results with low computational cost. A proposal to circumvent potential convergence issues of the original algorithm is presented and validated for the case where it occurs.

cond-mat.stat-mech↗
arXiv2021

Correlations in a polymeric structure immersed in a magnetic solution

Polymers are among the most important materials in the modern society being found almost in every activity of our daily life. Understanding their chemical and physical properties lead to improvements of their usage. The correlation functions are one of most important quantities to understand a physical system. The characteristic way it behaves describe how the system fluctuates, and much of the progress achieved to understand complex systems has been due to their study. Of particular interest in polymer science are the space correlations which describe its mechanical behavior. In this work I study the stiffness of a polymer immersed in a magnetic medium and trapped in an optical tweezers. Using Monte Carlo simulations the correlation function along the chain and the force in the tweezers are obtained as a function of temperature and density of magnetic particles. The results show that the correlation decay has two regimes: an initial very fast decay of order the monomer-monomer spacing and a power law in the long distance regime. The power law exponent has a minimum at a temperature $T_{min}$ for any non zero density of magnetic particles indicating that the system is more correlated in this region. Using a formula for the persistence length derived from the WLC theory one observed that it has a maximum at the same temperature. These results suggest that the correlations in the system may be a combination of exponential and power law.

cond-mat.soft↗
arXiv2018

The fully frustrated XY model revisited: A new universality class

The two-dimensional ($2d$) fully frustrated Planar Rotator model on a square lattice has been the subject of a long controversy due to the simultaneous $Z_2$ and $O(2)$ symmetry existing in the model. The $O(2)$ symmetry being responsible for the Berezinskii - Kosterlitz - Thouless transition ($BKT$) while the $Z_2$ drives an Ising-like transition. There are arguments supporting two possible scenarios, one advocating that the loss of $Ising$ and $BKT$ order take place at the same temperature $T_{t}$ and the other that the $Z_2$ transition occurs at a higher temperature than the $BKT$ one. In the first case an immediate consequence is that this model is in a new universality class. Most of the studies take hand of some order parameter like the stiffness, Binder's cumulant or magnetization to obtain the transition temperature. Considering that the transition temperatures are obtained, in general, as an average over the estimates taken about several of those quantities, it is difficult to decide if they are describing the same or slightly separate transitions. In this paper we describe an iterative method based on the knowledge of the complex zeros of the energy probability distribution to study the critical behavior of the system. The method is general with advantages over most conventional techniques since it does not need to identify any order parameter \emph{a priori}. The critical temperature and exponents can be obtained with good precision. We apply the method to study the Fully Frustrated Planar Rotator ($PR$) and the Anisotropic Heisenberg ($XY$) models in two dimensions. We show that both models are in a new universality class with $T_{PR}=0.45286(32)$ and $T_{XY}=0.36916(16)$ and the transition exponent $ν=0.824(30)$ ($\frac{1}ν=1.22(4)$).

cond-mat.stat-mech↗
arXiv2017

Energy Probability Distribution Zeros: A Route to Study Phase Transitions

In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties. Numerically, the most common approaches are those based in Monte Carlo simulations together finite size scaling analysis. The use of Monte Carlo techniques requires the estimate of quantities like the specific heat or susceptibilities in a wide range of temperature or the construction of the density of states in large intervals of energy. Although many of these techniques are well developed they may be very time consuming when the system size becomes large enough. It should be suitable to have a method that could surpass those difficulties. In this work we present an iterative method to study the critical behavior of a system based on the partial knowledge of the complex Fisher zeros set of the partition function. The method is general with advantages over most conventional techniques since it does not need to identify any order parameter \emph{a priori}. The critical temperature and exponents can be obtained with great precision even in the most unamenable cases like the two dimensional $XY$ model. To test the method and to show how it works we applied it to some selected models where the transitions are well known: The 2D Ising, Potts and XY models and to a homopolymer system. Our choice cover systems with first order, continuous and Berezinskii-Kosterlitz-Thouless transitions as well as the homopolymer that has two pseudo-transitions. The strategy can easily be adapted to any model, classical or quantum, once we are able to build the corresponding energy probability distribution.

cond-mat.stat-mech↗
arXiv2016

Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition

Using the two dimensional $XY-(S(O(3))$ model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii-Kosterlitz-Thouless ($BKT$) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the $BKT$ class of universality. We obtain $T_{BKT}$ in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions $\mathfrak{Re}(T) \leq T_{BKT}$ and $\mathfrak{Re}(T) > T_{BKT}$ in the thermodynamic limit show that $\mathfrak{Im}(T)$ goes to zero in the former case and is finite in the last one.

cond-mat.stat-mech↗
arXiv2013

The phase transition in the anisotropic Heisenberg model with long range dipolar interactions

In this work we have used extensive Monte Carlo calculations to study the planar to paramagnetic phase transition in the two-dimensional anisotropic Heisenberg model with dipolar interactions (AHd) considering the true long-range character of the dipolar interactions by means of the Ewald summation. Our results are consistent with an order-disorder phase transition with unusual critical exponents in agreement with our previous results for the Planar Rotator model with dipolar interactions. Nevertheless, our results disagrees with the Renormalization Group results of Maier and Schwabl [PRB, 70, 134430 (2004)] and the results of Rapini et. al. [PRB, 75, 014425 (2007)], where the AHd was studied using a cut-off in the evaluation of the dipolar interactions. We argue that besides the long-range character of dipolar interactions their anisotropic character may have a deeper effect in the system than previously believed. Besides, our results shows that the use of a cut-off radius in the evaluation of dipolar interactions must be avoided when analyzing the critical behavior of magnetic systems, since it may lead to erroneous results.

cond-mat.stat-mech↗
arXiv2011

Phase transition in two-dimensional magnetic systems with dipolar interactions

In this work we have used extensive Monte Carlo calculations to study the planar to paramagnetic phase transition in the two-dimensional anisotropic Heisenberg model with dipolar interactions (AHd) considering the true long-range character of the dipolar interactions by means of the Ewald summation. Our results are consistent with an order-disorder phase transition with unusual critical exponents in agreement with our previous results for the Planar Rotator model with dipolar interactions. Nevertheless, our results disagrees with the Renormalization Group results of Maier and Schwabl [PRB, 70, 134430 (2004)] and the results of Rapini et. al. [PRB, 75, 014425 (2007)], where the AHd was studied using a cut-off in the evaluation of the dipolar interactions. We argue that besides the long-range character of dipolar interactions their anisotropic character may have a deeper effect in the system than previously believed. Besides, our results shows that the use of a cut-off radius in the evaluation of dipolar interactions must be avoided when analyzing the critical behavior of magnetic systems, since it may lead to erroneous results.

cond-mat.stat-mech↗
arXiv2010

Static and dynamic simulation in the classical two-dimensional anisotropic Heisenberg model

By using a simulated annealing approach, Monte Carlo and molecular-dynamics techniques we have studied static and dynamic behavior of the classical two-dimensional anisotropic Heisenberg model. We have obtained numerically that the vortex developed in such a model exhibit two different behaviors depending if the value of the anisotropy $λ$ lies below or above a critical value $λ_c$ . The in-plane and out-of-plane correlation functions ($S^{xx}$ and $S^{zz}$) were obtained numerically for $λ< λ_c$ and $λ> λ_c$ . We found that the out-of-plane dynamical correlation function exhibits a central peak for $λ> λ_c$ but not for $λ< λ_c$ at temperatures above $T_{BKT}$ .

cond-mat.stat-mech↗
arXiv2010

A model for vortex formation in magnetic nanodots

We use Monte Carlo simulation to study the vortex nucleation on magnetic nanodots at low temperature. In our simulations, we have considered a simple microscopic two-dimensional anisotropic Heisenberg model with term to describe the anisotropy due to the presence of the nanodot edge. We have considered the thickness of the edge, which was not considered in previous works, introducing a term that controls the energy associated to the edge. Our results clearly show that the thickness of the edge has a considerable influence in the vortex nucleation on magnetic nanodots. We have obtained the hysteresis curve for several values of the surface anisotropy and skin depth parameter ($ξ$). The results are in excellent agreement with experimental data.

cond-mat.stat-mech↗
arXiv2010

Diagram for vortex formation in quasi-two-dimensional magnetic dots

The existence of nonlinear objects of the vortex type in two-dimensional magnetic systems presents itself as one of the most promising candidates for the construction of nanodevices, useful for storing data, and for the construction of reading and writing magnetic heads. The vortex appears as the ground state of a magnetic nanodisk whose magnetic moments interact via dipole-dipole potential?. In this work it is investigated the conditions for the formation of vortices in nanodisks in triangular, square, and hexagonal lattices as a function of the size of the lattice and of the strength of the dipole interaction D. Our results show that there is a "transition" line separating the vortex state from a capacitor like state. This line has a finite size scaling form depending on the size, L, of the system as Dc=D0 +1/A(?1+B*L^2)?. This behavior is obeyed by the three types of lattices. Inside the vortex phase it is possible to identify two types of vortices separated by a constant, D=Dc, line: An in-plane and an out-of-plane vortex. We observed that the out-of-plane phase does not appear for the triangular lattice. In a two layer system the extra layer of dipoles works as an effective out-of-plane anisotropy inducing a large S^z component at the center of the vortex. Also, we analyzed the mechanism for switching the out-of-plane vortex component. Contrary to some reported results, we found evidences that the mechanism is not a creation-annihilation vortex anti-vortex process.

cond-mat.stat-mech↗
arXiv2010

Phase transition in ultrathin magnetic films with long-range interactions: Monte Carlo simulation of the anisotropic Heisenberg model

Ultrathin magnetic films can be modeled as an anisotropic Heisenberg model with long-range dipolar interactions. It is believed that the phase diagram presents three phases: An ordered ferromagnetic phase I, a phase characterized by a change from out-of-plane to in-plane in the magnetization II, and a high-temperature paramagnetic phase III. It is claimed that the border lines from phase I to III and II to III are of second order and from I to II is first order. In the present work we have performed a very careful Monte Carlo simulation of the model. Our results strongly support that the line separating phases II and III is of the BKT type.

cond-mat.stat-mech↗
arXiv2010

Phase diagram of the antiferromagnetic XY model in two dimensions in a magnetic field

The phase diagram of the quasi-two-dimensional easy-plane antiferromagnetic model, with a magnetic field applied in the easy plane, is studied using the self-consistent harmonic approximation. We found a linear dependence of the transition temperature as a function of the field for large values of the field. Our results are in agreement with experimental data for the spin-1 honeycomb compound BaNi_2V_2O_3

cond-mat.stat-mech↗
arXiv2009

Phase transition in the two-dimensional dipolar Planar Rotator model

In this work we have used extensive Monte Carlo simulations and finite size scaling theory to study the phase transition in the dipolar Planar Rotator model (dPRM), also known as dipolar XY model. The true long-range character of the dipolar interactions were taken into account by using the Ewald summation technique. Our results for the critical exponents does not fit those from known universality classes. We observed that the specific heat is apparently non-divergent and the critical exponents are $ν=1.277(2)$, $β=0.2065(4)$ and $γ=2.218(5)$. The critical temperature was found to be $T_c=1.201(1)$. Our results are clearly distinct from those of a recent Renormalization Group study from Maier and Schwabl [PRB 70, 134430 (2004)] and agrees with the results from a previous study of the anisotropic Heisenberg model with dipolar interactions in a bilayer system using a cut-off in the dipolar interactions [PRB 79, 054404 (2009)].

cond-mat.stat-mech↗
arXiv2009

Magnetic monopole and string excitations in a two-dimensional spin ice

We study the magnetic excitations of a square lattice spin-ice recently produced in an artificial form, as an array of nanoscale magnets. Our analysis, based upon the dipolar interaction between the nanomagnetic islands, correctly reproduces the ground-state observed experimentally. In addition, we find magnetic monopole-like excitations effectively interacting by means of the usual Coulombic plus a linear confining potential, the latter being related to a string-like excitation binding the monopoles pairs, what indicates that the fractionalization of magnetic dipoles may not be so easy in two dimensions. These findings contrast this material with the three-dimensional analogue, where such monopoles experience only the Coulombic interaction. We discuss, however, two entropic effects that affect the monopole interactions: firstly, the string configurational entropy may loose the string tension and then, free magnetic monopoles should also be found in lower dimensional spin ices; secondly, in contrast to the string configurational entropy, an entropically driven Coulomb force, which increases with temperature, has the opposite effect of confining the magnetic defects.

cond-mat.mtrl-sci↗
arXiv2007

Velocity, temperature and normal force dependence on friction: An analytical and molecular dynamic study

In this work we propose an extension to the analytical one-dimensional model proposed by E. Gnecco (Phys. Rev. Lett. 84:1172) to describe friction. Our model includes normal forces and the dependence with the angular direction of movement in which the object is dragged over a surface. The presence of the normal force in the model allow us to define judiciously the friction coefficient, instead of introducing it as an {\sl a posteriori} concept. We compare the analytical results with molecular dynamics simulations. The simulated model corresponds to a tip sliding over a surface. The tip is simulated as a single particle interacting with a surface through a Lennard-Jones $(6-12)$ potential. The surface is considered as consisting of a regular BCC(001) arrangement of particles interacting with each other through a Lennard-Jones $(6-12)$ potential. We investigate the system under several conditions of velocity, temperature and normal forces. Our analytical results are in very good agreement with those obtained by the simulations and with experimental results from E. Riedo (Phys. Rev. Lett. 91:084502) and Eui-Sung Yoon (Wear 259:1424-1431) as well.

physics.comp-ph↗