Ground states and defect energies of the two-dimensional XY spin glass from a quasiexact algorithm

Martin Weigel, M. J P Gingras

Research output: Contribution to journalArticle

Abstract

We employ a novel algorithm using a quasiexact embedded-cluster matching technique as minimization method within a genetic algorithm to reliably obtain numerically exact ground states of the Edwards-Anderson XY spin-glass model with bimodal coupling distribution for square lattices of up to 28×28 spins. Contrary to previous conjectures, the ground state of each disorder replica is nondegenerate up to a global O(2) rotation. The scaling of spin and chiral defect energies induced by applying several different sets of boundary conditions exhibits strong crossover effects. This suggests that previous calculations have yielded results far from the asymptotic regime. The novel algorithm and the aspect-ratio scaling technique consistently give ?s=-0.308(30) and ?c=-0.114(16) for the spin and chiral stiffness exponents, respectively. © 2006 The American Physical Society.

Original languageEnglish
Article number097206
Pages (from-to)4-
JournalPhysical Review Letters
Volume96
Issue number9
DOIs
Publication statusPublished - 2006

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abstract = "We employ a novel algorithm using a quasiexact embedded-cluster matching technique as minimization method within a genetic algorithm to reliably obtain numerically exact ground states of the Edwards-Anderson XY spin-glass model with bimodal coupling distribution for square lattices of up to 28×28 spins. Contrary to previous conjectures, the ground state of each disorder replica is nondegenerate up to a global O(2) rotation. The scaling of spin and chiral defect energies induced by applying several different sets of boundary conditions exhibits strong crossover effects. This suggests that previous calculations have yielded results far from the asymptotic regime. The novel algorithm and the aspect-ratio scaling technique consistently give ?s=-0.308(30) and ?c=-0.114(16) for the spin and chiral stiffness exponents, respectively. {\circledC} 2006 The American Physical Society.",
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Ground states and defect energies of the two-dimensional XY spin glass from a quasiexact algorithm. / Weigel, Martin; Gingras, M. J P.

In: Physical Review Letters, Vol. 96, No. 9, 097206, 2006, p. 4-.

Research output: Contribution to journalArticle

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AB - We employ a novel algorithm using a quasiexact embedded-cluster matching technique as minimization method within a genetic algorithm to reliably obtain numerically exact ground states of the Edwards-Anderson XY spin-glass model with bimodal coupling distribution for square lattices of up to 28×28 spins. Contrary to previous conjectures, the ground state of each disorder replica is nondegenerate up to a global O(2) rotation. The scaling of spin and chiral defect energies induced by applying several different sets of boundary conditions exhibits strong crossover effects. This suggests that previous calculations have yielded results far from the asymptotic regime. The novel algorithm and the aspect-ratio scaling technique consistently give ?s=-0.308(30) and ?c=-0.114(16) for the spin and chiral stiffness exponents, respectively. © 2006 The American Physical Society.

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