arXiv subjects

L. N. Jorge

Publications and source records attributed to L. N. Jorge.

8 recordsLinked to original sources

arXiv2025

Berezinskii-Kosterlitz-Thouless transition in the XY model on the honeycomb lattice: A comprehensive Monte Carlo analysis

In this paper, we thoroughly examined the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional XY model on the honeycomb lattice. To address its thermodynamical behavior, we combined standard numerical Monte Carlo simulations with the simulated annealing (SA) protocol and entropic simulations based on the Wang-Landau (WL) algorithm. The transition temperature was determined using the second ($Υ$) and fourth-order ($Υ_4$) helicity modulus as the order parameter. Our best finite-size scaling analysis suggests $T_{BKT} = 0.575(8)$ from SA and $T_{BKT}=0.576(3)$ from WL. These values deviate significantly from the expected theoretical value of $1/\sqrt{2}$. We believe that this discrepancy suggests that the theoretical assumptions regarding the analytical calculation may need to be revisited. Additionally, we calculated the vortex density and the formation energy of the vortex-antivortex pairs, where the obtained vortex formation energy is $2μ=5.80(12)$. Upon comparison with the square lattice, our results support the notion of instability of the honeycomb lattice to support the spin long-range order and give additional backing to the critical behavior we found.

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↗

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

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↗