A Monte Carlo Approach for Studying Microphases Applied to the Axial Next-Nearest-Neighbor Ising and the Ising-Coulomb Models

Abstract

The equilibrium phase behavior of microphase-forming systems is notoriously difficult to obtain because of the extended metastability of their modulated phases. In this paper we present a systematic simulation methodology for studying layered microphases and apply the approach to two prototypical lattice-based systems: the three-dimensional axial next-nearest-neighbor Ising (ANNNI) and Ising-Coulomb (IC) models. The method involves thermodynamically integrating along a reversible path established between a reference system of free spins under an ordering field and the system of interest. The resulting free energy calculations unambiguously locate the phase boundaries. The simple phases are not observed to play a particularly significant role in the devil's flowers. With the help of generalized order parameters, the paramagnetic-modulated critical transition of the ANNNI model is also studied. We confirm the XY universality of the paramagnetic-modulated transition and its isotropic nature. Interfacial roughening is found to play at most a small role in the ANNNI layered regime.

15 pages, 11 figures, 2 tables

References in corpus (12)

• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Appearance of fluctuating stripes at the onset of the pseudogap in the high-Tc Superconductor Bi2Sr2CaCu2O8+x
• Phase behavior of a fluid with competing attractive and repulsive interactions
• Soft Spheres Make More Mesophases
• Colloidal systems with competing interactions: from an arrested repulsive cluster phase to a gel
• Structural and dynamical features of multiple metastable glassy states in a colloidal system with competing interactions
• Phase coexistence of cluster crystals: beyond the Gibbs phase rule
• Phase behavior and far-from-equilibrium gelation of charged attractive colloids
• Lamellar order, microphase structures and glassy phase in a field theoretic model for charged colloids
• Monte Carlo Study of the Axial Next-Nearest-Neighbor Ising Model
• Ground-State Shapes and Structures of Colloidal Domains
• Comment on: Competing Interactions, the Renormalization Group, and the Isotropic-Nematic Phase Transition, by D. Barci and D. Stariolo, Phys. Rev. Lett. 98, 200604 (2007)

Cited by in corpus (10)

• Equilibrium Phase Behavior of a Continuous-Space Microphase Former
• Recent Advances in the Theory and Simulation of Model Colloidal Microphase Formers
• Equilibrium phase behavior of the square-well linear microphase-forming model
• Universality of modulation length (and time) exponents
• [N]pT Monte Carlo Simulations of the Cluster-Crystal-Forming Penetrable Sphere Model
• Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field
• Topological floating phase in a spatially anisotropic frustrated Ising model
• Solution of Disordered Microphases in the Bethe approximation
• Magnetic field-induced deformation of the spin-density wave microphases in Ca${}_3$Co${}_2$O${}_6$
• Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model