arXiv subjects

Claudio J. DaSilva

Publications and source records attributed to Claudio J. DaSilva.

3 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↗

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↗

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↗