Determination of the critical exponents in the Ag Mn spin glass

Bouchiat, H.

doi:10.1051/jphys:0198600470107100

Cited by 132 publications

(84 citation statements)

References 28 publications

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“…The critical temperatures are consistent with previous results. Our values of ν sg and η sg are also consistent with those of the canonical sg materials [43][44][45]. This evidence suggests that the Heisenberg spin-glass model explains the experiments.…”

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confidence: 86%

From measurements to inferences of physical quantities in numerical simulations

Nakamura

2016

Phys. Rev. E

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We propose a change of style for numerical estimations of physical quantities from measurements to inferences. We estimate the most probable quantities for all the parameter region simultaneously by using the raw data cooperatively. Estimations with higher precisions are made possible. We can obtain a physical quantity as a continuous function, which is differentiated to obtain another quantity. We applied the method to the Heisenberg spin-glass model in three dimensions. A dynamic correlation-length scaling analysis suggests that the spin-glass and the chiral-glass transitions occur at the same temperature with a common exponent ν. The value is consistent with the experimental results. We found that a size-crossover effect explains a spin-chirality separation problem.Introduction-Estimations of physical quantities in numerical simulations are based on equilibrium statistical physics [1]. We virtualize a model system in a computer and perform independent measurements on the system using a definition of a physical quantity. When an evaluation process is complex, both systematic and statistical errors are accumulated in the obtained data. We sometimes encounter numerical instabilities, which may affect a final physical conclusion. In what follows, we explain the situation of interest using a correlation-length estimation.An estimation formula for a correlation length, ξ, is given by the second-moment method:. Here, χ 0 denotes the susceptibility and χ k its Fourier transform with k as the lowest wave number of the system. This expression itself is problematic. Both numerator and denominator of this expression approach zero as the system size increases (k → 0), where this formula becomes exact. We encounter the numerical instability caused by the expression 0/0. In order to avoid this problem, Bellettiet al. [3] proposed the reduction of this instability by estimating ξ through the integrals I k = 0 drr k f (r) and ξ is obtained as I 2 /I 1 . Suwa and Todo [4] proposed a generalized moment method for gap (∆ ∼ 1/ξ) estimation in quantum systems. Systematic errors and ambiguity caused by using small-L data are eliminated.Recently, big-data handling has become possible due to rapid increase in computational power. Data science is now one of the most promising fields in science and technology. As regards its application to physics, the topic of Bayesian inference has attracted considerable interest [5,6]. In this context, Harada [7] introduced Bayesian inference into a parameter estimation of the finite-size scaling analysis.In this paper, we extend its application to estimations of physical quantities. For example, we can obtain an analytic expression for an energy out of the discrete raw data as the most-probable model function. Then, we obtain the specific heat by analytically differentiating it. A critical temperture is estimated automatically within this procedure. Since directly-observed (raw) data are

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confidence: 86%

From measurements to inferences of physical quantities in numerical simulations

Nakamura

2016

Phys. Rev. E

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“…In conclusion, the critical exponents in a dipole-dipole interacting magnetic nanoparticle system have been determined for the first time using static scaling analysis of the nonlinear susceptibility. The inherent properties of a magnetic particle system imply that the scaling analysis must be performed at comparably large reduced temperatures which may yield higher apparent values of the critical exponents [20]. However, according to extensive MC simulations on an Ising spin-glass system, the critical region is found to extend up to reduced temperatures e ഠ 0.55 [18].…”

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confidence: 99%

Static Scaling on an Interacting Magnetic Nanoparticle System

1998

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“…This symmetry breaking, arising from an electron-nucleus weak interaction, has been observed in elements [2,3] eg. , Kr, Tl, Pb, Bi, and Cs.…”

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confidence: 96%

“…The observable nuclear properties such as binding energy (BE), neutron, and proton root-mean-square radii (r and r") and magnetic moments are calculated from the self-consistent solution of Eqs. (3).…”

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confidence: 99%

Relativistic mean-field approach to anapole moment: Atomic parity-violating hyperfine transitions

1995

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A generalized formula of nuclear anapole moment is derived using the current relativistic nuclear approach. The Dirac spin magnetization and the anomalous spin magnetization contributions to anapole moment are shown to be proportional to the second moment of respective magnetizations. The valence nucleon effective g~(g ) factors in a nucleus are obtained from the different phenomenological generalizations of relativistic nuclear magnetic moment. The unitary transformation approach is used to derive the parity nonconserving (PNC) perturbed wave functions. In the case of g~p arametrization, the anomalous spin magnetization and pion contributions to anapole moment are nearly two and three times the Dirac magnetization contribution respectively; while for g parametrization, all the three contributions are of the same order of magnitude. Using these calculated values of anapole moment and available atomic structure data from published literature, the Cs PNC hyper6ne amplitudes are calculated. The results are closer to the experimental data, particularly when the measured value of ImE~~' /P is used. The optical rotation angles induced by nuclear spin dependent PNC interaction are also calculated.

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Determination of the critical exponents in the Ag Mn spin glass

Cited by 132 publications

References 28 publications

From measurements to inferences of physical quantities in numerical simulations

From measurements to inferences of physical quantities in numerical simulations

Static Scaling on an Interacting Magnetic Nanoparticle System

Relativistic mean-field approach to anapole moment: Atomic parity-violating hyperfine transitions

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