Binder cumulants

The Binder cumulant , also called Binder parameter , according to the physicist Kurt Binder , is a quantity from statistical physics . It is defined as the fourth order cumulant of the order parameter - such as the magnetization : ${\displaystyle s}$

${\displaystyle U_{L}=1-{\frac {{\langle s^{4}\rangle }_{L}}{3{\langle s^{2}\rangle }_{L}^{2}}}}$

where is the linear dimension of the grid . ${\displaystyle L}$

With the help of the binder cumulants, the critical temperature during a phase transition can be determined very precisely. The cumulant also provides the value of the critical exponent of the correlation length , which characterizes the universality class of the phase transition.

The Binder Cumulant is widely used to reliably analyze data obtained in Monte Carlo simulations for a variety of models, including Ising , Heisenberg, and Potts models .

The numerical value of the binder cumulants at the critical point depends in the thermodynamic limit on the boundary conditions , the shape of the lattice and the anisotropy of the correlations.

literature

Kurt Binder, Dieter W. Heermann: Monte Carlo Simulation in Statistical Physics: An Introduction . Springer-Verlag, Berlin, ISBN 3-540-19107-0 .

Individual evidence

1. ↑ ^{a b} K. Binder , Z. Physik B: Condens. Matter, 43, 119 (1981); Phys. Rev. Lett. 47, 693 (1981)
2. ↑ G. Kamieniarz, HWJBlöte, J.Phys. A 26, 201 (1993)
3. ↑ XS Chen, V. Dohm , Phys. Rev. E70, 056136 (2004)
4. ↑ W. Selke , LN Shchur, J. Phys. A 38, L739 (2005)