Structure of Gibbs states of one dimensional Coulomb systems, Comm. Math. Phys, vol.78, issue.1, pp.99-116, 1980. ,
Binary crystals in two-dimensional two-component yukawa mixtures, J. Chem. Phys, vol.129, p.164511, 2008. ,
One-dimensional Ising model and the complete devil's staircase, Phys. Rev. Lett, vol.49, issue.4, pp.249-251, 1982. ,
Approximate global minimizers to pairwise interaction problems via convex relaxation, SIAM J. Appl. Dyn. Syst, vol.17, issue.1, pp.417-456, 2018. ,
Tret'yakov. Order and chaos in classical models of spin chains, Zh. Eksp. Teor. Fiz, vol.87, pp.310-322, 1984. ,
Two-dimensional Theta Functions and Crystallization among Bravais Lattices, SIAM J. Math. Anal, vol.48, issue.5, pp.3236-3269, 2016. ,
On the optimality of the rock-salt structure among lattices and change distributions, 2020. ,
Crystallization to the square lattice for a two-body potential, 2019. ,
Periodicity of the infinite-volume ground state of a one-dimensional quantum model, Nonlinear Anal, vol.48, issue.6, pp.791-803, 2002. ,
The Crystallization Conjecture: A Review, EMS Surv. in Math. Sci, vol.2, pp.255-306, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01139322
Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma, Functional integration and its applications, 1975. ,
Sorting phenomena in a mathematical model for two mutually attracting/repelling species, SIAM J. Math. Anal, vol.50, issue.3, pp.3210-3250, 2018. ,
Zoology of a non-local cross-diffusion model for two species, SIAM J. Appl. Math, vol.78, issue.2, pp.1078-1104, 2018. ,
Universally optimal distribution of points on spheres, J. Amer. Math. Soc, vol.20, issue.1, pp.99-148, 2007. ,
Universal optimality of the e 8 and leech lattices and interpolation formulas, 2019. ,
Crystallization in the hexagonal lattice for ionic dimers, Math. Models Methods Appl. Sci, vol.29, issue.10, pp.1853-1900, 2019. ,
Finite crystallization and Wulff shape emergence for ionic compounds in the square lattice, Nonlinearity, vol.33, issue.3, pp.1240-1296, 2020. ,
Crystallization in a one-dimensional periodic landscape, J. Stat. Phys, vol.179, pp.485-501, 2020. ,
The Infinite-Volume Ground State of the Lennard-Jones Potential, J. Stat. Phys, vol.20, pp.719-724, 1979. ,
Ising models with long-range dipolar and short range ferromagnetic interactions, Phys. Rev. B, vol.74, p.64420, 2006. ,
Periodic striped ground states in ising models with competing interactions, Comm. Math. Phys, vol.347, pp.983-1007, 2016. ,
Generalized Wigner lattices in one dimension and some applications to tetracyanoquinodimethane (TCNQ) salts, Phys. Rev. B, vol.17, issue.2, pp.494-505, 1978. ,
Surface energy and boundary layers for a chain of atoms at low temperature, 2019. ,
Magnetic domains in thin films with strong perpendicular anisotropy, Arch. Ration. Mech. Anal, vol.232, pp.727-761, 2019. ,
Crystalline structures in a 1-d two-component lattice gas with 1/r ? interactions, J. Stat. Mech. Theory Exp, p.33111, 2016. ,
Why do ultrasoft repulsive particles cluster and crystallize? analytical results from dens. funct. theory, J. Chem. Phys, vol.126, p.224502, 2007. ,
Two-species particle aggregation and stability of codimension one solutions, Disc. Cont. Dyn. Syst. B, vol.19, issue.5, pp.1411-1436, 2014. ,
On the properties of monolayers of adsorbed atoms, J. Phys. C: Solid State Phys, vol.11, pp.3535-3549, 1978. ,
, Encyclop. Dict.of Cond. Mat. Phys, 2004.
Crystals and quasicrystals: a continuum model, Comm. Math. Phys, vol.105, pp.385-390, 1986. ,
, 1d log gases and the renormalized energy: crystallization at vanishing temperature. Prob. Theory and Rel. Fields, vol.162, pp.795-846, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01076972
Atomic structure and dynamic behaviour of truly one-dimensional ionic chains inside carbon nanotubes, Nat. Mater, vol.13, pp.1050-1054, 2014. ,
Magnetic nanoparticles: recent advances in synthesis, self-assembly and applications, J. Mat. Chem, vol.21, issue.42, pp.16819-16845, 2011. ,
Ground State at High Density, Comm. Math. Phys, vol.305, pp.657-710, 2011. ,
Competing Interactions and Pattern Formation in Nanoworld, 2007. ,
On the Configuration of Systems of Interacting Particle with Minimum Potential Energy per Particle, Phys. A, vol.92, p.343, 1978. ,
On the Configuration of Systems of Interacting Particle with Minimum Potential Energy per Particle, Phys. A, vol.99, pp.569-580, 1979. ,