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Monte Carlo simulations of the three-dimensional X Y spin glass focusing on chiral and spin order

Monte Carlo simulations of the three-dimensional X Y spin glass focusing on chiral and spin order The ordering of the three-dimensional isotropic XY spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. To investigate the ordering of the spin and the chirality, we compute several independent physical quantities including the glass order parameter, the Binder parameter, the correlation-length ratio, the overlap distribution, and the non-self-averageness parameter, etc., for both the spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of spin-chirality decoupling, i.e., that the CG and SG order occur at two separate temperatures, 0 < T SG < T CG , is obtained from the glass order parameter, and is fully corroborated by the Binder parameter. By contrast, the CG correlation-length ratio yields a rather pathological and inconsistent result in the range of sizes we studied, which may originate from the finite-size effect associated with a significant short-length dropoff of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents ν CG = 1 . 36 − 0.37 + 0.15 and η CG = 0 . 26 − 0.26 + 0.29 , and the SG exponents ν SG = 1 . 22 − 0.06 + 0.26 and η SG = − 0 . 54 − 0.52 + 0.24 . The exponents obtained are close to those of the Heisenberg SG, but are very different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replica-symmetry breaking (1RSB), consistently with previous reports. Such a 1RSB feature is again like that of the Heisenberg SG, but is different from the Ising SG, which may be the cause of the difference in the CG critical properties from those of the Ising SG despite the common Z 2 symmetry. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

Monte Carlo simulations of the three-dimensional X Y spin glass focusing on chiral and spin order

Obuchi, Tomoyuki; Kawamura, Hikaru
Physical Review B , Volume 87 (17) – May 31, 2013
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References (5)

Publisher
American Physical Society (APS)
Copyright
©2013 American Physical Society
ISSN
1098-0121
DOI
10.1103/PhysRevB.87.174438
Publisher site
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Abstract

The ordering of the three-dimensional isotropic XY spin glass with nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. To investigate the ordering of the spin and the chirality, we compute several independent physical quantities including the glass order parameter, the Binder parameter, the correlation-length ratio, the overlap distribution, and the non-self-averageness parameter, etc., for both the spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of spin-chirality decoupling, i.e., that the CG and SG order occur at two separate temperatures, 0 < T SG < T CG , is obtained from the glass order parameter, and is fully corroborated by the Binder parameter. By contrast, the CG correlation-length ratio yields a rather pathological and inconsistent result in the range of sizes we studied, which may originate from the finite-size effect associated with a significant short-length dropoff of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents ν CG = 1 . 36 − 0.37 + 0.15 and η CG = 0 . 26 − 0.26 + 0.29 , and the SG exponents ν SG = 1 . 22 − 0.06 + 0.26 and η SG = − 0 . 54 − 0.52 + 0.24 . The exponents obtained are close to those of the Heisenberg SG, but are very different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replica-symmetry breaking (1RSB), consistently with previous reports. Such a 1RSB feature is again like that of the Heisenberg SG, but is different from the Ising SG, which may be the cause of the difference in the CG critical properties from those of the Ising SG despite the common Z 2 symmetry.

Journal

Physical Review B – American Physical Society (APS)

Published: May 31, 2013

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