The triangular Ising antiferromagnet in a staggered field

We study the equilibrium properties of the nearest-neighbor Ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states. Using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice, we classify the ground states into sectors specified by the number of ``strings''. We show that the effect of the staggered field is to generate long-range interactions between strings. In the limiting case of the antiferromagnetic coupling constant J becoming infinitely large, we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature. For finite J, we study the equilibrium properties of the system using Monte Carlo simulations with three different dynamics. We find that in all the three cases, equilibration times for low field values increase rapidly with system size at low temperatures. Due to this difficulty in equilibrating sufficiently large systems at low temperatures, our finite-size scaling analysis of the numerical results does not permit a definite conclusion about the existence of a phase transition for finite values of J. A surprising feature in the system is the fact that unlike usual glassy systems, a zero-temperature quench almost always leads to the ground state, while a slow cooling does not.Comment: 12 pages, 18 figures: To appear in Phys. Rev.

Self-induced and induced transparencies of two-dimensional and three- dimensional superlattices

The phenomenon of transparency in two-dimensional and three-dimensional superlattices is analyzed on the basis of the Boltzmann equation with a collision term encompassing three distinct scattering mechanisms (elastic, inelastic and electron-electron) in terms of three corresponding distinct relaxation times. On this basis, we show that electron heating in the plane perpendicular to the current direction drastically changes the conditions for the occurrence of self-induced transparency in the superlattice. In particular, it leads to an additional modulation of the current amplitudes excited by an applied biharmonic electric field with harmonic components polarized in orthogonal directions. Furthermore, we show that self-induced transparency and dynamic localization are different phenomena with different physical origins, displaced in time from each other, and, in general, they arise at different electric fields.Comment: to appear in Physical Review

Phase transition in spin systems with various types of fluctuations

Various types ordering processes in systems with large fluctuation are overviewed. Generally, the so-called order–disorder phase transition takes place in competition between the interaction causing the system be ordered and the entropy causing a random disturbance. Nature of the phase transition strongly depends on the type of fluctuation which is determined by the structure of the order parameter of the system. As to the critical property of phase transitions, the concept “universality of the critical phenomena” is well established. However, we still find variety of features of ordering processes. In this article, we study effects of various mechanisms which bring large fluctuation in the system, e.g., continuous symmetry of the spin in low dimensions, contradictions among interactions (frustration), randomness of the lattice, quantum fluctuations, and a long range interaction in off-lattice systems

Effective scatterings between electrons, excitons and trions

The final goal of this paper is to derive the effective scattering ruling the time evolution of two semiconductor trions using the many-body formalism for composite fermions we have just proposed. However, to understand the importance of the particle composite nature, their bosonic/fermionic character and their overall charge, we also report on scatterings between free electrons, excitons and trions. This leads us to identify the form factors associated to direct processes involving excitons and trions. For transitions between ground states, these form factors reduce to zero and one respectively, in the small momentum transfer limit. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011