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Designer spin systems via inverse statistical mechanics. II. Ground-state enumeration and classification

Author(s): Marcotte, Étienne; DiStasio, Robert A.; Stillinger, Frank H.; Torquato, Salvatore

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Abstract: ©2013 American Physical Society. In the first paper of this series [DiStasio, Jr., Marcotte, Car, Stillinger, and Torquato, Phys. Rev. B 88, 134104 (2013)], we applied inverse statistical-mechanical techniques to study the extent to which targeted spin configurations on the square lattice can be ground states of finite-ranged radial spin-spin interactions. In this sequel, we enumerate all of the spin configurations within a unit cell on the one-dimensional integer lattice and the two-dimensional square lattice up to some modest size under periodic boundary conditions. We then classify these spin configurations into those that can or cannot be unique classical ground states of the aforementioned radial pair spin interactions and found the relative occurrences of these ground-state solution classes for different system sizes. As a result, we also determined the minimal radial extent of the spin-spin interaction potentials required to stabilize those configurations whose ground states are either unique or degenerate (i.e., those sharing the same radial spin-spin correlation function). This enumeration study has established that unique ground states are not limited to simple target configurations. However, we also found that many simple target spin configurations cannot be unique ground states.
Publication Date: 1-Nov-2013
Electronic Publication Date: 27-Nov-2013
Citation: Marcotte, Étienne, DiStasio, Robert A., Stillinger, Frank H., Torquato, Salvatore. (2013). Designer spin systems via inverse statistical mechanics. II. Ground-state enumeration and classification. Physical Review B, 88 (18), 10.1103/PhysRevB.88.184432
DOI: doi:10.1103/PhysRevB.88.184432
ISSN: 1098-0121
EISSN: 1550-235X
Pages: 88.18:184432-1 - 184432-14
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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