Minos A. Neto

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 clusters we calculate the phase diagrams in the H−T and Ω−T planes for the square lattice. We have only found second order phase transitions for all values of fields and reentrant behavior was not observed.

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 (F) nearest-neighbor interactions (J1) and antiferromagnetic (AF) next-nearest-neighbor couplings (J2) are analyzed in the plane temperature versus α, where α = J2/|J1| is the frustration parameter. We used the original Wang–Landau sampling (WLS) 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 re-entrant behavior, observed in the frontier separating the F and the collinear order, is an artifact of the EFT approach and should disappear when we consider Monte Carlo (MC) simulations of the model. In addition, our results indicate that the continuous phase transition between the F and the paramagnetic (P) phases, that occurs for 0.0 ≤α< 0.25, belongs to the universality class of the three-dimensional pure Ising Model.

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 monomer 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 by comparing the location of the maximum of the specific heat with the exact results and conventional Wang–Landau simulations for the three types of walk.

Reentrance in the phase diagrams of the transverse Ising antiferromagnet in the presence of the longitudinal magnetic field on a simple cubic lattice

In this paper, we study the critical behavior of the three-dimensional antiferromagnetic Ising model in both uniform longitudinal (H) and transverse (?) magnetic fields. Using the effective field theory (EFT) with finite cluster N?=?1 spin (EFT) we calculate the phase diagrams in the H?T, ??T and ??H planes for a simple cubic lattice. We have only found second-order phase transitions for all values of fields and reentrant behavior was observed at low temperature.

A new effective correlation mean-field theory for the ferromagnetic spin-1 Blume–Capel model in a transverse crystal field

A new approximation technique is developed so as to study the quantum ferromagnetic spin-1 Blume–Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by noninteracting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low-temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is computationally costly.

Ferromagnetic phases due to competing short- and long-range interactions in the spin-5/2 and spin-2 Blume–Capel model

Abstract We broaden the study of the statistical physics of the spin-S Blume–Capel model with ferromagnetic mean-field interactions J in competition with short-range antiferromagnetic interactions K in a linear chain in the thermodynamic limit. This work is dedicated to the case when S takes the half-integer spin S = 5 / 2 and when S assumes the integer value S = 2 . In both cases the phase diagrams exhibit new ferromagnetic phases (for certain values of K) enclosed by branches emerging from the first-order frontiers of the pure ferromagnetic model. For finite temperatures the complex topologies were obtained by numerical minimization of the free energy and some results were confirmed by Monte Carlo simulations.

Cooper-pair size and binding energy for unconventional superconducting systems

Abstract The main proposal of this paper is to analyze the size of the Cooper pairs composed by unbalanced mass fermions from different electronic bands along the BCS–BEC crossover and study the binding energy of the pairs. We are considering an interaction between fermions with different masses leading to an inter-band pairing. In addiction to the attractive interaction we have an hybridization term to couple both bands, which in general acts unfavorable for the pairing between the electrons. We get first order phase transitions as the hybridization breaks the Cooper pairs for the s -wave symmetry of the gap amplitude. The results show the dependence of the Cooper-pair size as a function of the hybridization for T = 0 . We also propose the structure of the binding energy of the inter-band system as a function of the two-bands quasi-particle energies.

Spin-1/2 anisotropic Heisenberg antiferromagnet model with Dzyaloshinskii-Moriya interaction via mean-field approximation

Abstract The spin-1/2 anisotropic Heisenberg model with antiferromagnetic exchange interactions in the presence of a longitudinal external magnetic field and a Dzyaloshinskii-Moriya interaction is studied by employing the usual mean-field approximation. The magnetic properties are obtained and it is shown that only second-order phase transitions take place for any values of the theoretical Hamiltonian parameters. Contrary to previous results from effective field theory, no anomalies have been observed at low temperatures. However, some reentrancies still persist in some region of the phase diagram.

Multicritical behavior of the two-dimensional transverse Ising metamagnet in a longitudinal magnetic field

Magnetic phenomena of the two-dimensional anisotropic antiferromagnetic Ising model in both uniform longitudinal (H) and uniform transverse (Ω) magnetic fields are studied by employing a mean-field variational approach based on Bogoliubov inequality for the free energy. The phase diagrams in the magnetic fields and temperature (T) planes, namely H−T and Ω−T, are analyzed on an anisotropic square lattice for some values of the ratio α=Jy/Jx, where Jx and Jy are, respectively, the exchange interactions along the x and y directions. Depending on the range of the Hamiltonian parameters, one has only second-order transition lines, only first-order transition lines, or both first- and second-order transition lines with the presence of tricritical points. In addition, the corresponding phase diagrams are free from any reentrant behavior.