arXiv subjects

A. A. Caparica

Publications and source records attributed to A. A. Caparica.

16 recordsLinked to original sources

arXiv2024

2D triangular Ising model with bond phonons: An entropic simulation study

In this work, we study and evaluate the impact of a periodic spin-lattice coupling in an Ising-like system on a 2D triangular lattice. Our proposed simple Hamiltonian considers this additional interaction as an effect of preferential phonon propagation direction augmented by the symmetry ofthe underline lattice. The simplified analytical description of this new model brought us consistent information about its ground state and thermal behavior, and allowed us to highlight a singularity where the model behaves as several decoupled one-dimensional Ising systems. A thorough analysis was obtained via entropic simulations based in the Wang-Landau method that estimates the density of states g(E) to explore the phase diagram and other thermodynamic properties of interest. Also, we used the finite size scaling technique to characterize the critical exponents and the nature of the phase transitions that, despite the strong influence of the spin-lattice coupling, turned out to be within the same universality class as the original 2D Ising model.

cond-mat.stat-mech↗

arXiv2022

An entropic approach to analyze phase transitions in the q = 3 Potts model

Boltzmann's microcanonical entropy is the link between statistical physics and thermodynamics, forasmuch as the behavior of any thermodynamic quantity is directly related to the number of microscopic configurations. Accordingly, in this work, we investigate the behavior of the logarithm of the density of states of the three-state Potts model with an external field applied to one of the states using joint entropic simulations based on the Wang-Landau algorithm. Our analysis reveals that the microcanonical entropy curve is detachable, and each resulting path is related to the formation of clusters. Such a description is consistent with the energy-entropy argument related to the inception of a phase transition. When the external field is reversed and strong, the observed phase transition is from an ordered configuration to cluster formations. The behavior of the microcanonical inverse temperature indicates both first and second-order phase transitions occurring at different temperatures for high values of the external field.

cond-mat.stat-mech↗

arXiv2021

Rotational symmetry breaking potential for two-dimensional magnets

Here we present a new perspective to the breakdown of ferromagnetic order in two-dimensional spin-lattice models employing the rotation of the underlying lattice. Using an Ising spin system on a square lattice as a prototype, we demonstrate that an additional low-symmetry interaction may lead to the absence of the truly long-range order and forms aperiodic structure, such as magnetic stripes. Employing annealing and entropic Monte Carlo simulations, we show that our model allows tuning between different phases, magnetically ordered as well as more exotic nonmagnetic phases such as Ising-nematic by changing only one control parameter, which is responsible for the arising of magnetic frustration. In addition, our methodology of considering the coupling between the magnetic structure and the host material can be extended to the study of any type of spin-exchange model in two dimensions and has many potential interesting ramifications and applications.

cond-mat.stat-mech↗

arXiv2020

An entropic simulational study of the spin-$1$ Baxter-Wu model in a crystal field

We investigate the critical behavior of the two-dimensional spin-$1$ Baxter-Wu model in a crystal field using entropic sampling simulations with the joint density of states. We obtain the temperature-crystal field phase diagram, which includes a tetracritical line ending at a pentacritical point. A finite-size scaling analysis of the maximum of the specific heat, while changing the crystal field anisotropy, is used to obtain a precise location of the pentacritical point. Our results give the critical temperature and crystal field as $T_{pc}=0.98030(10)$ and $D_{pc}=1.68288(62)$. We also detect that at the first-order region of the phase diagram, the specific heat exhibits a double peak structure as in the Schottky-like anomaly, which is associated with an order-disorder transition.

cond-mat.stat-mech↗

arXiv2020

Thoroughly analysis of the phase diagram for the Bell-Lavis model: An entropic simulational study

In this work, we investigate the Bell-Lavis model using entropic simulations for several values of the energy parameters. The $T\timesμ$ phase diagram and the ground state configurations are analyzed thoroughly. Besides, we examine the particle density and specific heat behavior for different values of the chemical potential $μ$ as functions of temperature. We also obtain configurations that maximize the canonical probability for several values of chemical potential and temperature, enabling the identification of the low density ($LDL$) and high-density liquid ($HDL$) phases, among others, in the critical regions. We found a second-order phase transition from the $LDL-HDL_0$ to $LDL-HDL$ coexistence in the range of $0<μ<1.05503$. In the $1.05503<μ<1.48024$ range, the transition between the $LDL-HDL_0$ and $LDL-HDL_0-empty$ coexistence presents discontinuous and continuous transitions characteristics. Finally, for $1.48024<μ<1.5$, the phase transition between $LDL$ and $empty$ phases is of first-order.

cond-mat.stat-mech↗

arXiv2020

Unveiling phase transitions in 1D systems with short-range interactions

The statement that any phase transition is related to the appearance or disappearance of long-range spatial correlations precludes a finite transition temperature in one-dimensional (1D) systems. In this paper we demonstrate that the 1D Ising model with short-range exchange interactions exhibits a second-order phase transition at a finite temperature relying on the proper choice of the order parameter. To accomplish this, we combined analytical calculations and high-precision entropic sampling simulations and chose a slightly different order parameter, namely the module of the magnetization. Notably, we detected a phase transition with a corresponding critical temperature around 15 K, which is in excellent agreement with experimental results. Our study indicates that an inappropriate choice of the order parameter may mask phase transitions in one-dimensional systems.

cond-mat.stat-mech↗

arXiv2018

The three-dimensional Baxter-Wu Model

A classic three-dimensional spin model, based upon the Baxter-Wu scheme, is presented. It is found, by entropic sampling simulations, that the behavior of the energy and magnetization fourth-order cumulants points out to a first order phase transition. A finite-size procedure was performed, confirming that the system scales with the dimensionality d = 3, and yielding a high-resolution estimate of the critical temperature as T c = 11.377577(39).

cond-mat.stat-mech↗

arXiv2018

On the order of the phase transition in the spin-1 Baxter-Wu model

In this work we investigate the order of the phase transition of the spin-1 Baxter-Wu model. We used extensive entropic simulations to describe the behavior of quantities which reveal the order of the phase transition. We applyied finite-sizing scaling laws for continuous and discontinuous phase transitions. Our results show that this system exhibits an indeterminacy regarding the order of the phase transition, i.e., the results are conclusive for both transitions, whether continuous or discontinuous. In such a scenario we carried out a study of the configurations in the region of the phase transition, which confirmed that the model seems to undergo a tetracritical transition, with the coexistence of a ferromagnetic and three ferrimagnetic configurations, suggesting that it may be a multicritical point belonging to a critical line of an external or a crystalline fields, where the continuous and the discontinuous phase transitions may coexist reflecting different features of the system

cond-mat.stat-mech↗

arXiv2016

Non-equilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line

We investigate the short-time universal behavior of the two dimensional Ashkin-Teller model at the Baxter line by performing time-dependent Monte Carlo Simulations. First, as preparatory results, we obtain the critical parameters by searching the optimal power law decay of the magnetization. Thus, the dynamic critical exponents $θ_{m}$ and $θ_{p}$, related to the magnetic and electric order parameters, as well as the persistence exponent $θ_{g}$, are estimated using heat-bath Monte Carlo simulations. In addition, we estimate the dynamic exponent $z$ and the static critical exponents $β$ and $ν$ for both order parameters. We propose a refined method to estimate the static exponents that considers two different averages: one that combines an internal average using several seeds with another which is taken over geographic variations in the power laws. Moreover, we also performed the bootstrapping method for a complementary analysis. Our results show that the ratio $β/ν$ exhibits universal behavior along the critical line corroborating the conjecture for both magnetization and polarization.

cond-mat.stat-mech↗

arXiv2016

Critical behavior of the spin-$1/2$ Baxter-Wu model: Entropic sampling simulations

In this work we use a refined entropic sampling technique based on the Wang-Landau method to study the spin-$1/2$ Baxter-Wu model. The static critical exponents were determined as $α=0.6545(68)$, $β=0.0818(30)$, $γ=1.18193(77)$, and $ν=0.66341(47)$. The estimate for the critical temperature was $T_c=2.269194(45)$. We compare the present results with those obtained from other well established approaches and we find a startling closeness with the exact values, besides the high precision reached for the critical temperature. We also calculate the coefficients $a$ and $b$ for the divergence of the microcanonical inverse temperature at the ground state achieving an excellent agreement in comparison with the simulation estimates.

physics.comp-ph↗

arXiv2015

Static critical behavior of the $q-$states Potts model: High-resolution entropic study

Here we report a precise computer simulation study of the static critical properties of the two-dimensional $q$-states Potts model using very accurate data obtained from a modified Wang-Landau (WL) scheme proposed by Caparica and Cunha-Netto [Phys. Rev. E {\bf 85}, 046702 (2012)]. This algorithm is an extension of the conventional WL sampling, but the authors changed the criterion to update the density of states during the random walk and established a new procedure to windup the simulation run. These few changes have allowed a more precise microcanonical averaging which is essential to a reliable finite-size scaling analysis. In this work we used this new technique to determine the static critical exponents $β$, $γ$, and $ν$, in an unambiguous fashion. The static critical exponents were determined as $β=0.10807(28)$, $γ=1.44716(72)$, and $ν=0.818892(58)$, for the $q=3$ case, and $β=0.09123(48)$, $γ=1.2855(13)$, and $ν=0.70640(10)$, for the $q=4$ Potts model. A comparison of the present results with conjectured values and with those obtained from other well established approaches strengthens this new way of performing WL simulations.

cond-mat.stat-mech↗

arXiv2008

Two-dimensional lattice polymers: adaptive windows simulations

We report a numerical study of self-avoiding polymers on the square lattice, including an attractive potential between nonconsecutive monomers. Using Wang-Landau sampling (WLS) with adaptive windows, we obtain the density of states for chains of up to N=300 monomers and associated thermodynamic quantities. The method enables one to simulate accurately the low-temperature regime, which is virtually inaccessible using traditional methods. Instead of defining fixed energy windows, as in usual WLS, this method uses windows with boundaries that depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor $f$ is reduced, we eliminate border effects that arise in simulations using fixed windows.

cond-mat.stat-mech↗

arXiv2008

Improving Wang-Landau sampling with adaptive windows

Wang-Landau sampling (WLS) of large systems requires dividing the energy range into "windows" and joining the results of simulations in each window. The resulting density of states (and associated thermodynamic functions) are shown to suffer from boundary effects in simulations of lattice polymers and the five-state Potts model. Here, we implement WLS using adaptive windows. Instead of defining fixed energy windows (or windows in the energy-magnetization plane for the Potts model), the boundary positions depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor f is reduced, we eliminate border effects that arise in simulations using fixed windows. Adaptive windows extend significantly the range of system sizes that may be studied reliably using WLS.

cond-mat.stat-mech↗

arXiv2006

An alternative order parameter for the 4-state Potts model

We have investigated the dynamic critical behavior of the two-dimensional 4-state Potts model using an alternative order parameter first used by Vanderzande [J. Phys. A: Math. Gen. \textbf{20}, L549 (1987)] in the study of the Z(5) model. We have estimated the global persistence exponent $θ_g$ by following the time evolution of the probability $P(t)$ that the considered order parameter does not change its sign up to time $t$. We have also obtained the critical exponents $θ$, $z$, $ν$, and $β$ using this alternative definition of the order parameter and our results are in complete agreement with available values found in literature.

cond-mat.stat-mech↗

arXiv2006

Wang-Landau sampling in three-dimensional polymers

Monte Carlo simulations using Wang-Landau sampling are performed to study three-dimensional chains of homopolymers on a lattice. We confirm the accuracy of the method by calculating the thermodynamic properties of this system. Our results are in good agreement with those obtained using Metropolis importance sampling. This algorithm enables one to accurately simulate the usually hardly accessible low-temperature regions since it determines the density of states in a single simulation.

cond-mat.stat-mech↗

arXiv2006

Short-time behavior of a classical ferromagnet with double-exchange interaction

We investigate the critical dynamics of a classical ferromagnet on the simple cubic lattice with double-exchange interaction. Estimates for the dynamic critical exponents $z$ and $θ$ are obtained using short-time Monte Carlo simulations. We also estimate the static critical exponents $ν$ and $β$ studying the behavior of the samples at an early time. Our results are in good agreement with available estimates and support the assertion that this model and the classical Heisenberg model belong to the same universality class.

cond-mat.stat-mech↗