# Formation of Stripes and Slabs Near the Ferromagnetic Transition

@article{Giuliani2014FormationOS, title={Formation of Stripes and Slabs Near the Ferromagnetic Transition}, author={Alessandro Giuliani and Elliott H. Lieb and Robert Seiringer}, journal={Communications in Mathematical Physics}, year={2014}, volume={331}, pages={333-350} }

We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)−p, p > 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value Jc, then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to Jc, the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as $${J…

## 14 Citations

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### One-dimensional minimizers for a diffuse interface generalized antiferromagnetic model in general dimension

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### Exact Periodic Stripes for Minimizers of a Local/Nonlocal Interaction Functional in General Dimension

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We study the functional considered in Giuliani et al. (Phys Rev B 84:064205, 2011, Commun Math Phys 331(1):333–350, 2014) and Giuliani and Seiringer (Commun Math Phys 347:983–1007, 2016) and a…

### Exact Periodic Stripes for Minimizers of a Local/Nonlocal Interaction Functional in General Dimension

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We study the functional considered in Giuliani et al. (Phys Rev B 84:064205, 2011, Commun Math Phys 331(1):333–350, 2014) and Giuliani and Seiringer (Commun Math Phys 347:983–1007, 2016) and a…

### On the optimality of stripes in a variational model with non-local interactions

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We study pattern formation for a variational model displaying competition between a local term penalizing interfaces and a non-local term favoring oscillations. By means of a $$\Gamma $$Γ-convergence…

### The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling

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We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the two-dimensional triangular lattice. The system is fully frustrated and displays two families of ground…

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