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词条 Binder parameter
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  1. References

The Binder parameter or Binder cumulant[1] in statistical physics, also known as the fourth-order cumulant is defined as the kurtosis of the order parameter, s. It is frequently used to determine accurately phase transition points in numerical simulations of various models. [2]

The phase transition point is usually identified comparing the

behavior of as a function of the temperature for different values of the system size . The transition temperature is the unique point where the different curves cross in the thermodynamic limit. This behavior is based on the fact that

in the critical region, , the Binder parameter behaves as , where .

Accordingly, the cumulant may also be used to identify the universality class of the transition by determining the value of the critical exponent of the correlation length. [1]

In the thermodynamic limit, at the critical point, the value of the Binder parameter depends on boundary conditions, the shape of the system, and anisotropy of correlations.

[1][3][4][5]

References

1. ^K. Binder, Z. Phys. B 43, 119 (1981); Phys.Rev. Lett. 47, 693 (1981)
2. ^K. Binder, D. W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction (2010) Springer
3. ^G. Kamieniarz, H.W.J.Blöte, J.Phys. A 26, 201 (1993)
4. ^ X. S. Chen, V. Dohm, Phys. Rev. E70, 056136 (2004)
5. ^W.Selke, L.N. Shchur, J. Phys. A 38, L739 (2005)

1 : Statistical mechanics

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