Related papers: Taming geometric frustration by leveraging structu…

The resolution of geometric frustration in systems with continuous degrees of freedom often involves a cooperative inhomogeneous response and super-extensive energy scaling. In contrast, the frustration in frustrated Ising-like spin systems…

Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that cannot be realized globally. Recently, such frustrated assemblies were shown to exhibit filamentation, size limitation, large…

Geometric frustration results from a discrepancy between the locally favored arrangement of the constituents of a system and the geometry of the embedding space. Geometric frustration can be either non-cumulative, which implies an extensive…

Geometric frustration and the ice rule are two concepts that are intimately connected and widespread across condensed matter. The first refers to the inability of a system to satisfy competing interactions in the presence of spatial…

Geometric frustration arises when lattice structure prevents simultaneous minimization of local interactions. It leads to highly degenerate ground states and, subsequently, complex phases of matter such as water ice, spin ice and frustrated…

The concept of geometrical frustration in condensed matter physics refers to the fact that a system has a locally preferred structure with an energy density lower than the infinite ground state. This notion is however often used in a…

Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical…

Topological frustration arises when boundary conditions impose geometric frustration in a quantum system, creating delocalized defects in the ground states and profoundly altering the low-energy properties. While previous studies have been…

Geometrically frustrated assemblies where building blocks misfit have been shown to generate intriguing phenomena from self-limited growth, fiber formation, to structural complexity. We introduce a graph theory formulation of geometrically…

In self-assembling systems, geometric frustration leads to complex states characterized by internal gradients of shape misfit. Frustrated assemblies have drawn recent interest due to the unique possibility that their thermodynamics can…

Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry1-7. Geometric frustration gives rise to new fundamental phenomena and is…

This perspective will overview an emerging paradigm for self-organized soft materials, {\it geometrically-frustrated assemblies}, where interactions between self-assembling elements (e.g. particles, macromolecules, proteins) favor local…

Geometric frustration is recognized to generate complex morphologies in self-assembling particulate and molecular systems. In bulk states, frustrated drives structured arrays of topological defects. In the dilute limit, these systems have…

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, display rich behaviours not found elsewhere in nature. Artificial spin ice takes a materials-by-design approach to studying…

Coarsening dynamics theory has successfully described the equilibration of a broad class of systems.By studying the relaxation of a periodic array of microcondensates immersed in a Fermi gas which can mediate long-range spin interactions to…

After a short introduction on frustrated spin systems, we study in this chapter several two-dimensional frustrated Ising spin systems which can be exactly solved by using vertex models. We show that these systems contain most of the…

The Ising model, often seen as the paradigmatic spin model, has been heavily studied for its mathematical description of ferromagnetism in statistical mechanics. We explore a quantum version of this model, the transverse field Ising model,…

The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure…

Dense systems of active matter exhibit highly dynamic collective motion characterized by intermingled vortices, referred to as active turbulence. The interaction between these vortices is key to controlling turbulent dynamics, and a…

Geometric frustration lies at the heart of many unconventional quantum phases in strongly interacting electron systems. Here, we analytically determine the ground state magnetization of the half-filled Hubbard model on frustrated geometries…