We focus on the statistical and thermodynamic properties of systems with
competing long-range interactions. The studies are based on the physics of quasi-one dimensional
system with special interest towards their topological defects, the so-called solitons. We have
been considering ensembles of solitons resulting from the degeneracy of the ground state of
the system. This is the case of various charge density-wave systems such as polyacetylene-like
polymers where the solitons are the non-trivial excitations connecting different ground-states.
We have been interested in particular with a one component plasma with $3D$ Coulomb
interactions of such defects, mainly in 2 space dimensions. The $3D$ case has also been
considered. The quasi-one dimensional nature of the system is responsible for the confinement
of the solitons. This competition between confinement and Coulomb has been formulated
and some of its non-trivial effects analyaed. This led us to study the statistical properties of
charged interfaces: strings or domain walls in $3D$. We have found that shape instabilities, due
to the competing interactions, play a fundamental role. The obtained results show similarities
with experimental work in the field of stripe phases in cuprate oxides.
Light-Induced Anisotropic Skyrmion and Stripe Phases in a Rashba Ferromagnet
