A Scaling Hypothesis for Modulated Systems

Abstract

We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $\alpha$ of the inverse distance. With L being a spatial length characterizing the modulated phase, all thermodynamic quantities are predicted to scale like some power of L. The scaling dimensions with respect to L only depend on the dimensionality of the system d and the exponent α. Scaling predictions are in agreement with experiments on ultra-thin ferromagnetic films and computational results. Finally, our scaling hypothesis implies that, for some range of values α>d, Inverse-Symmetry-Breaking transitions may appear systematically in the considered class of frustrated systems.

13 pages, 6 figures, expanded version

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• Periodic striped ground states in Ising models with competing interactions
• Inverse transition in the two dimensional dipolar frustrated ferromagnet
• A Quantum-Classical Model of Brain Dynamics
• Coarse grained models of stripe forming systems: phase diagrams, anomalies and scaling hypothesis
• On the mechanism behind the inverse melting in systems with competing interactions
• Nematic Phase in two-dimensional frustrated systems with power law decaying interactions
• Formation of stripes and slabs near the ferromagnetic transition
• Finite temperature phase diagram of ultrathin magnetic films without external fields
• Modulated phases in external fields: when is reentrant behavior to be expected?
• Topological phase diagrams of the frustrated Ising ferromagnet
• Domain-wall free energy in Heisenberg ferromagnets
• Inverse transition in the dipolar frustrated Ising ferromagnet: the role of domain walls
• On the coexistence of dipolar frustration and criticality in ferromagnets
• The frustrated spherical model: an alternative to Ginzburg-Landau Hamiltonians with competing interactions