Modulation and correlations lengths in systems with competing interactions

Abstract

We examine correlation functions in the presence of competing long and short ranged interactions to find multiple correlation and modulation lengths. We calculate the ground state stripe width of an Ising ferromagnet, frustrated by an arbitrary long range interaction. In large $n$ systems, we demonstrate that for a short range system frustrated by a general competing long range interaction, the crossover temperature $T^{\ast }$ veers towards the critical temperature of the unfrustrated short range system (i.e., that in which the frustrating long range interaction is removed). We also show that apart from certain special crossover points, the total number of correlation and modulation lengths remains conserved. We derive an expression for the change in modulation length with temperature for a general system near the ground state with a ferromagnetic interaction and an opposing long range interaction. We illustrate that the correlation functions associated with the exact dipolar interactions differ substantially from those in which a scalar product form between the dipoles is assumed.

17 pages, 9 figures

References in corpus (6)

• Ising models with long-range dipolar and short-range ferromagnetic interactions
• Surface Geometric and Electronic Structure of BaFe2As2(001)
• Striped phases in two dimensional dipole systems
• Orientational order in two dimensions from competing interactions at different scales
• Stripe width and non-local domain walls in the two-dimensional Dipolar Frustrated Ising Ferromagnet
• High temperature correlation functions: universality, extraction of exchange interactions, divergent correlation lengths and generalized Debye length scales

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