Alejandro Mendoza-Coto

Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions

We study two dimensional stripe forming systems with competing repulsive interactions decaying as r(-α). We derive an effective Hamiltonian with a short-range part and a generalized dipolar interaction which depends on the exponent α. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for α<2 long-range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When α≥2 no long-range order is possible, but a phase transition in the Kosterlitz-Thouless universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids (α=1) and dipolar magnetic films (α=3). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.

Modulated systems in external fields: Conditions for the presence of reentrant phase diagrams

Alejandro Mendoza-Coto, Orlando V. Billoni, ∗ Sergio A. Cannas, † and Daniel A. Stariolo ‡ Departamento de F́ısica, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970, Porto Alegre, Brazil Facultad de Matemática, Astronomı́a, F́ısica y Computación, Universidad Nacional de Córdoba, Instituto de F́ısica Enrique Gaviola (IFEG-CONICET) Ciudad Universitaria, 5000 Córdoba, Argentina Departamento de F́ısica, Universidade Federal Fluminense and National Institute of Science and Technology for Complex Systems Av. Gal. Milton Tavares de Souza s/n, Campus Praia Vermela, 24210-346 Niterói, RJ, Brazil (Dated: February 20, 2018)

Langevin simulations of stripe forming systems with long-range isotropic competing interactions

We address the critical properties of the isotropic-nematic phase transition in stripe forming systems. We focus on isotropic models in which a short range attractive interaction competes with a long range repulsive interaction decaying as a power-law, paying particular attention to the cases in which this interaction is of dipolar or Coulomb types. Using Langevin dynamics simulations we show that these models belong to different universality classes. The numerical algorithms developed for each case are presented and discussed in detail. The obtained results are in agreement with recent theoretical predictions [1], according to which the orientational transition belongs to the Kosterlitz-Thouless universality class for dipolar systems, while it is of the second-order type for Coulomb systems.

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real time dynamics of a large class of classical markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Coarse-grained models of stripe forming systems: phase diagrams, anomalies, and scaling hypothesis.

Two coarse-grained models which capture some universal characteristics of stripe forming systems are studied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence of generic isotropic competing interactions. Although this is known to lead to some universal properties, we show that the phase diagrams have important differences, which are a consequence of the particular k dependence of the fluctuation spectrum in each model. The phase diagrams are computed in a mean field approximation and also after inclusion of small fluctuations, which are shown to modify drastically the mean field behavior. Observables like the modulation length and magnetization profiles are computed for the whole temperature range accessible to both models and some important differences in behavior are observed. A stripe compression modulus is computed, showing an anomalous behavior with temperature as recently reported in related models. Also, a recently proposed scaling hypothesis for modulated systems is tested and found to be valid for both models studied.

Quantum and thermal melting of stripe forming systems with competing long-range interactions

We study the quantum melting of stripe phases in models with competing short range and long range interactions decaying with distance as

Asymptotic dynamics of a frustrated model with spherical constraint

1/r^{\sigma}

On the mechanism behind the inverse melting in systems with competing interactions

in two space dimensions. At zero temperature we find a two step disordering of the stripe phases with the growth of quantum fluctuations. A quantum critical point separating a phase with long range positional order from a phase with long range orientational order is found when

Mendoza-Coto, Stariolo, and Nicolao Reply:

\sigma \leq 4/3

Stripe forming systems in an external field: when is reentrant behavior to be expected?

, which includes the Coulomb interaction case