Colloquium: Ice rule and emergent frustration in particle ice and beyond

Antonio Ortiz-Ambriz, Cristiano Nisoli, Charles Reichhardt, Cynthia J. O. Reichhardt, and Pietro Tierno
Rev. Mod. Phys. 91, 041003 – Published 30 December 2019

Abstract

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 constraints. The second, in its more general sense, represents a prescription for the minimization of the topological charges in a constrained system. Both can lead to manifolds of high susceptibility and nontrivial, constrained disorder where exotic behaviors can appear and even be designed deliberately. This Colloquium describes the emergence of geometric frustration and the ice rule in soft condensed matter. It excludes the extensive developments of mathematical physics within the field of geometric frustration, but rather focuses on systems of confined microscopic or mesoscopic particles that emerge as a novel paradigm exhibiting spin degrees of freedom. In such systems, geometric frustration can be engineered artificially by controlling the spatial topology and geometry of the lattice, the position of the individual particle units, or their relative filling fraction. These capabilities enable the creation of novel and exotic phases of matter and also potentially lead toward technological applications related to memory and logic devices that are based on the motion of topological defects. The rapid progress in theory and experiments is reviewed and the intimate physical connections with other frustrated systems at different length scales are discussed.

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  • Received 7 June 2019

DOI:https://doi.org/10.1103/RevModPhys.91.041003

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Antonio Ortiz-Ambriz

  • Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028, Barcelona, Spain and Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028, Barcelona, Spain

Cristiano Nisoli, Charles Reichhardt, and Cynthia J. O. Reichhardt

  • Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Pietro Tierno*

  • Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028, Barcelona, Spain, Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028, Barcelona, Spain, and Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028, Barcelona, Spain

  • *ptierno@ub.edu

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Issue

Vol. 91, Iss. 4 — October - December 2019

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