Monte Carlo Studies of the Two-Dimensional Random-Bond<i>X</i><i>Y</i>Model–A Chiral Spin Glass

Kawamura, Hikaru; Tanemura, Masaharu

doi:10.1143/jpsj.54.4479

Cited by 33 publications

(11 citation statements)

References 6 publications

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“…Numerical simulations on the vector SG, i.e., the twocomponent XY SG or the three-component Heisenberg SG, investigating both the spin and the chirality degrees of freedom, have been performed ever since 1985 28 . A crucially important concept which emerged from these studies is the possible "spin-chirality decoupling" phenomenon [29][30][31] .…”

Section: Introductionmentioning

confidence: 99%

“…Villain made a conjecture that the 3D XY SG might exhibit a finite-temperature SG ordering by noting the Ising nature of the chirality and by invoking the occurrence of a finite-temperature SG transition in the 3D Ising SG 27 . Numerical simulations on the vector SG, i.e., the twocomponent XY SG or the three-component Heisenberg SG, investigating both the spin and the chirality degrees of freedom, have been performed ever since 1985 28 . A crucially important concept which emerged from these studies is the possible "spin-chirality decoupling" phenomenon [29][30][31] .…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo simulations of the three-dimensionalXYspin glass focusing on chiral and spin order

Obuchi¹,

Kawamura²

2013

Phys. Rev. B

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The ordering of the three-dimensional isotropic XY spin glass with the 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 the spin-chirality decoupling, i.e., the CG and the SG order occurring at two separated temperatures, 0 < TSG < TCG, is obtained from the glass order parameter, which 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 drop-off of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents νCG = 1.36 +0.15 −0.37 and ηCG = 0.26 +0.29 −0.26 , and the SG exponents νSG = 1.22 +0.26 −0.06 and ηSG = −0.54 +0.24 −0.52 . The obtained exponents are close to those of the Heisenberg SG, but are largely different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replicasymmetry breaking (1RSB), consistently with the previous reports. Such a 1RSB feature is again in common with that of the Heisenberg SG, but is different from the Ising one, which may be the cause of the difference in the CG critical properties from the Ising SG ones despite of a common Z2 symmetry.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of the three-dimensionalXYspin glass focusing on chiral and spin order

Obuchi¹,

Kawamura²

2013

Phys. Rev. B

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“…XY-spin glasses are of special interest since they potentially exhibit two distinct kinds of ordering: spin glass ordering due to freezing of the spins, and "chiral glass" ordering due to freezing of local chiral (vortex) degrees of freedom. [8][9][10][11][12][13][14][15][16] It has been well established 17,18 that the spins do not have a finite temperature spin glass transition in three dimensions, whereas Kawamura 14,16 has argued that a finite temperature chiral glass transition does occur. This intriguing claim provides one of the main motivations for the present study.…”

Section: Introductionmentioning

confidence: 99%

Common universality class for the three-dimensional vortex glass and chiral glass

Wengel

Young

1997

Phys. Rev. B

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We present a Monte Carlo study of the d = 3 gauge glass and the XY-spin glass models in the vortex representation. We investigate the critical behavior of these models by a scaling analysis of the linear resistivity and current-voltage characteristics, both in the limits of zero and strong screening of the vortex-interactions. Without screening, both models show a glass transition at a finite temperature and, within the numerical accuracy, exhibit the same critical exponents: z ≈ 3.1 and ν = 1.3 ± 0.3. With strong screening, the finite temperature glass transition is destroyed in both cases and the same exponent ν = 1.05 ± 0.1 is found at the resulting zero temperature transition.

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“…Thus, for two-component XY spin systems including the XY SG, the z-component of the vector chirality κ z represents a discrete Z 2 chiral degeneracy [17,18,19], just as the scalar chirality χ represents a discrete Z 2 chiral degeneracy for three-component Heisenberg spin systems. Meanwhile, the vector chirality κ z of the XY spin exhibits different symmetry properties from the scalar chirality χ of the Heisenberg spin.…”

Section: Introductionmentioning

confidence: 99%

The ordering ofXYspin glasses

Kawamura¹

2011

J. Phys.: Condens. Matter

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Abstract. Ordering properties of XY -like spin-glass magnets with an easy-plane magnetic anisotropy are studied based on a symmetry consideration and the results of recent numerical simulations on the pure Heisenberg and XY spin-glass models. The effects of an easy-plane-type uniaxial anisotropy, a random magnetic anisotropy and an applied magnetic field are investigated. In the XY regime in zero field, the "spin-chirality decoupling" persists even under the random magnetic anisotropy, escaping the "spin-chirality recoupling" phenomenon which inevitably occurs in the Heisenberg regime. Contrast between the scalar chiral order and the vector chiral order is emphasized. Implications to experiments are discussed.

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Monte Carlo Studies of the Two-Dimensional Random-BondXYModel–A Chiral Spin Glass

Cited by 33 publications

References 6 publications

Monte Carlo simulations of the three-dimensionalXYspin glass focusing on chiral and spin order

Monte Carlo simulations of the three-dimensionalXYspin glass focusing on chiral and spin order

Common universality class for the three-dimensional vortex glass and chiral glass

The ordering ofXYspin glasses

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