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Competition between frustration and spin dimensionality in the classical antiferromagnetic $n$-vector model with arbitrary $n$

Nikolaos P. Konstantinidis

SciPost Phys. Core 6, 042 (2023) · published 8 June 2023


A new method to characterize the strength of magnetic frustration is proposed by calculating the minimum dimensionality of the absolute ground states of the classical nearest-neighbor antiferromagnetic $n$-vector model with arbitrary $n$. Platonic solids in three and four dimensions and Archimedean solids have lowest-energy configurations in a number of spin dimensions equal to their real-space dimensionality. Fullerene molecules and geodesic icosahedra can produce ground states in as many as five spin dimensions. Frustration is also characterized by the maximum value of the round-state energy when the exchange interactions are allowed to vary.

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