Field-dependent susceptibility of a spin glass

Simpson, Mitchell

doi:10.1088/0305-4608/9/7/018

Cited by 29 publications

(13 citation statements)

References 11 publications

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“…FIG. 19. A schematic form of the SG Binder parameter gSG in the thermodynamic limit, as expected in the present model.…”

Section: T Cg T Sgsupporting

confidence: 59%

“…Numerical simulations have been the main tool in attacking the issue. Although the existence of a finite-temperature SG transition was established in the 3D Ising EA model [5][6][7][8][9][10][11] , earlier numerical simulations on the 3D XY and the Heisenberg EA models suggested the absence of a finitetemperature transition [12][13][14][15][16][17][18] , in apparent contrast to experiments [19][20][21][22][23][24][25][26] .…”

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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“…FIG. 19. A schematic form of the SG Binder parameter gSG in the thermodynamic limit, as expected in the present model.…”

Section: T Cg T Sgsupporting

confidence: 59%

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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“…It should be stressed that, in contrast to a naive expectation mentioned above, the experimentally determined SG critical exponents of such weakly anisotropic Heisenberg-like SGs largely deviate from the exponent values of the 3D Ising EA model. Indeed, for typical canonical SG materials, consistent experimental estimates are now available thanks to careful experimental measurements [21,22,23,24,25,26,27]. The exponents determined by various authors for canonical SGs indeed come close to each other, yielding the values β ≃ 1, γ ≃ 2.2 − 2.3, ν ≃ 1.3 − 1.4 and η ≃ 0.4 − 0.5, which are clearly at odd with the exponent values of the 3D Ising EA model.…”

Section: Ordering In Zero Fieldmentioning

confidence: 99%

Two models of spin glasses — Ising versus Heisenberg

Kawamura

2010

J. Phys.: Conf. Ser.

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Brief review is given on recent numerical research of the ordering of two typical models of spin glasses (SGs), the three-dimensional (3D) Ising SG and the 3D Heisenberg SG models. Particular attention is paid to the questions of whether there is a thermodynamic transition in zero field, what are the associated critical properties, what is the nature of the ordered state, particularly of a possible replica-symmetry breaking, and whether there is a thermodynamic transition in applied fields. The properties of the two models are contrasted, and possible relation to experiments is discussed.

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“…Although critical exponents have been determined by many authors in the past, (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24) ours is the most complete analysis of the critical behavior of a spin glass reported so far and the first to determine boundaries of the critical region in both Hand T. However, we do not explicitly explore the possibility of a line of phase transitions in the H, T plane except at H = O. Although critical exponents have been determined by many authors in the past, (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24) ours is the most complete analysis of the critical behavior of a spin glass reported so far and the first to determine boundaries of the critical region in both Hand T. However, we do not explicitly explore the possibility of a line of phase transitions in the H, T plane except at H = O.…”

Section: Scaling Of Susceptibility and The Size Of The Critical Regiomentioning

confidence: 99%

Scaling of susceptibility and the size of the critical region in an amorphous GdAl spin glass (invited)

Malozemoff

Imry

Barbara

1982

Journal of Applied Physics

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We extend our earlier SQUID magnetometry studies of the susceptibility of amorphous Gd37A63 spin glass to a temperature range 5≤T≤100 K and a field range 0.5≤H<50 000 Oe. This enables us to determine the size of the critical region around the spin glass transition at TG=15.5 K; it extends to approximately 22 K in temperature and 15 000 Oe in field. We show that the range of reduced temperature t=(T−TG)/TG for spin glass critical behavior is determined by the parameter 1/Z1/2, where Z is the number of interacting neighbors, in rough agreement with experiment, and that the field range can be estimated from a crossover relation Hαtφ/2. We also find that nonanalyticity in χ(H) as H→0 persists at all temperatures below TG and argue that this can cause apparent nonanalyticity above TG as well in the presence of sample inhomogeneity.

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Field-dependent susceptibility of a spin glass

Cited by 29 publications

References 11 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

Two models of spin glasses — Ising versus Heisenberg

Scaling of susceptibility and the size of the critical region in an amorphous GdAl spin glass (invited)

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