The triangular universe.

Sci Am

Published: February 2007

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Geometric frustration in two-dimensional Ising models allows for a wealth of exotic universal behavior, both Ising and non-Ising, in the presence of quantum fluctuations. In particular, the triangular antiferromagnet and Villain model in a transverse field can be understood through distinct XY pseudospins, but have qualitatively similar phase diagrams including a quantum phase transition in the (2+1)-dimensional XY universality class. While the quantum dynamics of modestly-sized systems can be simulated classically using tensor-based methods, these methods become infeasible for larger lattices.

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Structures, or spatial arrangements of matter and energy, including some fields (e.g., velocity or pressure) are ubiquitous in research applications and frequently require description for subsequent analysis, or stochastic reconstruction from limited data.

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