arXiv subjects

Minos A. Neto

Publications and source records attributed to Minos A. Neto.

28 records · Page 2Linked to original sources

arXiv2016

Thermodynamic properties of rod-like chains: entropic sampling simulations

In this work we apply entropic sampling simulations to a three-state model which has exact solutions in the microcanonical and grand-canonical ensembles. We consider $N$ chains placed on an unidimensional lattice, such that each site may assume one of three-states: empty (state 1), with a single molecule energetically null (state 2), and with a single molecule with energy $\varepsilon$ (state 3). Each molecule, which we will treat here as dimers, consists of two monomers connected one to each other by a rod. The thermodynamic properties, such as internal energy, densities of dimers and specific heat were obtained as functions of temperature where the analytic results in the micro-canonical and grand-canonical ensembles were successfully confirmed by the entropic sampling simulations.

cond-mat.stat-mech↗

arXiv2016

The spin-3/2 Blume-Capel model with competing short- and long-range interactions

The phase diagrams of the spin-$3/2$ Blume-Capel model with competing short and long-range interactions were studied through the free energy density obtained by analytical methods. The competition emerges when positive short-range interactions of strength $K$ arranged in a linear chain tend to establish an anti-parallel spin order, whereas negative long-range interactions $-J$ tend to align them in parallel. Thus, no ferromagnetic order exists for $K/J > 0.25$. So, the phase-diagrams were scanned by varying the values of $K$ in this interval. As in other similar study done for the spin-1 case, the second-order frontier separating the ferromagnetic and the paramagnetic phases is transformed gradually into a first-order line, when $K/J$ is greater than a certain critical value. Accordingly, there is a subinterval of $K$, for which two tricritical points appear restricting the length of the second-order frontier. Nevertheless, for greater values of $K/J$, the ferromagnetic-paramagnetic frontier becomes wholly of first order. Also, the tipical coexistence line, which divides two different ferromagnetic phases of magnetization $m=3/2$ and $m=1/2$, becomes more complex by giving rise to another line of coexistence with a reentrant behavior that encloses a third ordered phase. In this case, the competition is such that there is a region in the phase diagram, where for each spin $i$ with $S_{i}=3/2$ ($S_{i}=-3/2$), there is another one spin $j$ with $S_{j}=-1/2$ ($S_{j}=1/2$), so the absolute value of the magnetization per spin is one.

cond-mat.stat-mech↗

arXiv2015

Magnetization plateaus in the antiferromagnetic Ising chain with single-ion anisotropy and quenched disorder

We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal-field and of the width of the distributions. For the Bernoulli distribution, the number of plateaus increases, with respect to the uniform case (F. Litaiff, J. R. de Sousa, and N. S. Branco, Sol. St. Comm. {\bf 147}, 494 (2008)) and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears, as the width increases.

cond-mat.stat-mech↗

arXiv2013

Qualitative aspects of the phase diagram of J1-J2 model on the cubic lattice

The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic nearest-neighbor interactions ($J_{1}$) and antiferromagnetic next-nearest-neighbor couplings ($J_{2}$) are analyzed in the plane temperature versus $α$, where $α=J_{2}/|J_{1}|$ is the frustration parameter. We used the original Wang-Landau sampling and the standard Metropolis algorithm to confront past results of this model obtained by the effective-field theory (EFT) for the cubic lattice. Our numerical results suggest that the predictions of the EFT are in general qualitatively correct, but the low-temperature reentrant behavior, observed in the frontier separating the ferromagnetic and the colinear order, is an artifact of the EFT approach and should disappear when we consider Monte Carlo simulations of the model. In addition, our results indicate that the continuous phase transition between the Ferromagnetic and the Paramagnetic phases, that occurs for $0.0 \leq α< 0.25$, belongs to the universality class of the three-dimensional pure Ising Model.

cond-mat.stat-mech↗

arXiv2013

Entropy of polydisperse chains: solution on the Husimi lattice

We consider the entropy of polydisperse chains placed on a lattice. In particular, we study a model for equilibrium polymerization, where the polydispersivity is determined by two activities, for internal and endpoint monomers of a chain. We solve the problem exactly on a Husimi lattice built with squares and with arbitrary coordination number, obtaining an expression for the entropy as a function of the density of monomers and mean molecular weight of the chains. We compare this entropy with the one for the monodisperse case, and find that the excess of entropy due to polydispersivity is identical to the one obtained for the one-dimensional case. Finally, we obtain a distribution of molecular weights with a rather complex behavior, but which becomes exponential for very large mean molecular weight of the chains, as required by scaling properties which should apply in this limit.

cond-mat.stat-mech↗

arXiv2012

Phase diagrams of the transverse Ising antiferromagnet in the presence of the longitudinal magnetic field

In this paper we study the critical behavior of the two-dimensional antiferromagnetic Ising model in both uniform longitudinal ($H$) and transverse ($Ω$) magnetic fields. Using the effective-field theory (EFT) with correlation in single site cluster we calculate the phase diagrams in the $H-T$ and $Ω-T$ planes for the square ($z=4$) lattices. We have only found second order phase transitions for all values of fields and reentrant behavior was not observed.

cond-mat.stat-mech↗

arXiv2012

The Rubber Band Revisited: Wang-Landau Simulation

In this work we apply Wang-Landau simulations to a simple model which has exact solutions both in the microcanonical and canonical formalisms. The simulations were carried out by using an updated version of the Wang-Landau sampling. We consider a homopolymer chain consisting of $N$ monomers units which may assume any configuration on the two-dimensional lattice. By imposing constraints to the moves of the polymers we obtain three different models. Our results show that updating the density of states only after every $N$ monomers moves leads to a better precision. We obtain the specific heat and the end-to-end distance per monomer and test the precision of our simulations comparing the location of the maximum of the specific heat with the exact results for the three types of walks.

cond-mat.stat-mech↗

arXiv2012

The Ising antiferromagnet on an anisotropic simple cubic lattice in the presence of a magnetic field

We have studied the anisotropic three-dimensional nearest-neighbor Ising model with competitive interactions in an uniform longitudinal magnetic field $H$. The model consists of ferromagnetic interaction $J_{x}(J_{z})$ in the $x(z)$ direction and antiferromagnetic interaction $J_{y}$ in the $y$ direction. We have compared our calculations within a effective-field theory in clusters with four spins (EFT-4) in the simple cubic (sc) lattice with traditional Monte Carlo (MC) simulations. The phase diagrams in the $h-k_{B}T/J_{x}$ plane ($h=H/J_{x}$) were obtained for the particular case $λ_{1}=J_{y}/J_{x} (λ_{2}=J_{z}/J_{x})=1$ (anisotropic sc). Our results indicate second-order frontiers for all values of $H$ for the particular case $λ_{2}=0$ (square lattice), while in case $λ_{1}=λ_{2}=1$, we observe first- and second-order phase transitions in the low and high temperature limits, respectively, with presence of a tricritical point. Using EFT-4, a reentrant behavior at low temperature was observed in contrast with results of MC.

cond-mat.stat-mech↗

arXiv2008

Entropy of polydisperse chains: solution on the Bethe lattice

We consider the entropy of polydisperse chains placed on a lattice. In particular, we study a model for equilibrium polymerization, where the polydispersivity is determined by two activities, for internal and endpoint monomers of a chain. We solve the problem exactly on a Bethe lattice with arbitrary coordination number, obtaining an expression for the entropy as a function of the density of monomers and mean molecular weight of the chains. We compare this entropy with the one for the monodisperse case, and find that the excess of entropy due to polydispersivity is identical to the one obtained for the one-dimensional case. Finally, we obtain an exponential distribution of molecular weights.

cond-mat.stat-mech↗

arXiv2008

An individual based model with global competition interaction: fluctuations effects in pattern formation

We present some numerical results obtained from a simple individual based model that describes clustering of organisms caused by competition. Our aim is to show how, even when a deterministic description developed for continuum models predicts no pattern formation, an individual based model displays well defined patterns, as a consequence of fluctuations effects caused by the discrete nature of the interacting agents.

cond-mat.stat-mech↗