Octavio D. Rodriguez Salmon

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.

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.