arXiv subjects

T. F. A. Alves

Publications and source records attributed to T. F. A. Alves.

22 records · Page 2Linked to original sources

arXiv2018

Logarithm corrections in the critical behavior of the Ising model on a triangular lattice modulated with the Fibonacci sequence

We investigated the critical behavior of the Ising model in a triangular lattice with ferro and anti-ferromagnetic interactions modulated by the Fibonacci sequence, by using finite-size numerical simulations. Specifically, we used a replica exchange Monte Carlo method, known as Parallel Tempering, to calculate the thermodynamic quantities of the system. We have obtained the staggered magnetization $q$, the associated magnetic susceptibility ($χ$) and the specific heat $c$, to characterize the universality class of the system. At the low-temperature limit, we have obtained a continuous phase transition with a critical temperature around $T_{c} \approx 1.4116$ for a particular modulation of the lattice according to the Fibonacci letter sequence. In addition, we have used finite-size scaling relations with logarithmic corrections to estimate the critical exponents $β$, $γ$ and $ν$, and the correction exponents $\hatβ$, $\hatγ$, $\hatα$ and $\hatλ$. Our results show that the system obeys the Ising model universality class and that the critical behavior has logarithmic corrections.

cond-mat.dis-nn↗

arXiv2017

Critical behavior of the 2D Ising model modulated by the Octonacci sequence

We investigated the Ising model on a square lattice with ferro and antiferromagnetic interactions modulated by the quasiperiodic Octonacci sequence in both directions of the lattice. We have applied the Replica Exchange Monte Carlo (Parallel Tempering) technique to calculate the thermodynamic quantities of the system. We obtained the order parameter, the associated magnetic susceptibility ($χ$) and the specific heat $(c)$ in order to characterize the universality class of the phase transition. Also, we use the finite size scaling method to obtain the critical temperature of the system and the critical exponents $β$, $γ$ and $ν$. In the low temperature limit we have obtained a continuous transition with critical temperature around $T_{c} \approx 1.413$. The system obeys the Ising universality class with logarithmic corrections. We found estimatives for the correction exponents $\hatβ$, $\hatγ$ and $\hatλ$ by using the finite size scaling technique.

cond-mat.stat-mech↗

arXiv2007

The anisotropic XY model on the inhomogeneous periodic chain

The static and dynamic properties of the anisotropic XY-model $(s=1/2)$ on the inhomogeneous periodic chain, composed of $N$ cells with $n$ different exchange interactions and magnetic moments, in a transverse field $h,$ are determined exactly at arbitrary temperatures. The properties are obtained by introducing the Jordan-Wigner fermionization and by reducing the problem to a diagonalization of a finite matrix of $nth$ order. The quantum transitions are determined exactly by analyzing, as a function of the field, the induced magnetization $1/n\sum_{m=1}^{n}μ_{m}\left< S_{j,m}^{z}\right>$ ($j$ denotes the cell, $m$ the site within the cell, $μ_{m}$ the magnetic moment at site $m$ within the cell) and the spontaneous magnetization $1/n\sum_{m=1}^{n}\left< S_{j,m}^{x},\right>$ which is obtained from the correlations $\left< S_{j,m}^{x}S_{j+r,m}^{x}\right>$ for large spin separations. These results, which are obtained for infinite chains, correspond to an extension of the ones obtained by Tong and Zhong(\textit{Physica B} \textbf{304,}91 (2001)). The dynamic correlations, $\left< S_{j,m}^{z}(t)S_{j^{\prime},m^{\prime}}^{z}(0)\right>$, and the dynamic susceptibility, $χ_{q}^{zz}(ω),$ are also obtained at arbitrary temperatures. Explicit results are presented in the limit T=0, where the critical behaviour occurs, for the static susceptibility $χ_{q}^{zz}(0)$ as a function of the transverse field $h$, and for the frequency dependency of dynamic susceptibility $χ_{q}^{zz}(ω)$.

cond-mat.stat-mech↗

arXiv2005

The isotropic XY model on the inhomogeneous periodic chain

The static and dynamic properties of the isotropic XY-model $(s=1/2)$ on the inhomogeneous periodic chain, composed of \emph{N} segments with \emph{n} different exchange interactions and magnetic moments, in a transverse field \emph{h} are obtained exactly at arbitrary temperatures. The properties are determined by introducing the generalized Jordan-Wigner transformation and by reducing the problem to a diagonalization of a finite matrix of \emph{n-th} order. The diagonalization procedure is discussed in detail and the critical behaviour induced by the transverse field, at T=0, is presented. The quantum transitions are determined by analyzing the behaviour of the induced magnetization, defined as $(1/n)\sum_{m=1}^{n}μ_{m} $ where $μ_{m}$ is the magnetic moment at site \emph{m} within the segment \emph{j}, as a function of the field, and the critical fields determined exactly. The dynamic correlations, $ $, and the dynamic susceptibility $χ_{q}^{zz}(ω)$ are also obtained at arbitrary temperatures. Explicit results are also presented in the limit T=0, where the critical behaviour occurs, for the static susceptibility $χ_{q}^{zz}(0)$ as a function of the transverse field \emph{h}, and for the frequency dependency of dynamic susceptibility $χ_{q}^{zz}(ω)$. Also in this limit, the transverse time-correlation $ $, the dynamic and isothermal susceptibilities, $χ_{q}^{xx}(ω)$ and $χ_{T}^{xx}$, are obtained for the transverse field greater or equal than the saturation field.

cond-mat.stat-mech↗