Binder cumulant: Difference between revisions

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(New page: {{Stub-general}} The '''Binder cumulant''' for an Ising model with zero field, is given by :<math>U_4 = 1- \frac{\langle m^4 \rangle }{3\langle m^2 \rangle^2 }</math> . ...)
 
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The '''Binder cumulant''' for an [[Ising Models |Ising model]] with zero field, is given by
The '''Binder cumulant''' for an [[Ising Models |Ising model]] with zero field, is given by


:<math>U_4 = 1- \frac{\langle m^4 \rangle }{3\langle m^2 \rangle^2 }</math> .
:<math>U_4 = 1- \frac{\langle m^4 \rangle }{3\langle m^2 \rangle^2 }</math>  


where ''m'' is the [[Order parameters |order parameter]].
In the [[thermodynamic limit]], where the system size <math>L \rightarrow \infty</math>, <math>U_4 \rightarrow 0</math> for <math>T > T_c</math>, and <math>U_4 \rightarrow 2/3</math> for <math>T < T_c</math>.
In the [[thermodynamic limit]], where the system size <math>L \rightarrow \infty</math>, <math>U_4 \rightarrow 0</math> for <math>T > T_c</math>, and <math>U_4 \rightarrow 2/3</math> for <math>T < T_c</math>.


==References==
==References==
#[http://dx.doi.org/10.1007/BF01293604 K. Binder "Finite size scaling analysis of ising model block distribution functions", Zeitschrift für Physik B Condensed Matter '''43''' pp. 119-140 (1981)]
#[http://dx.doi.org/10.1007/BF01293604 K. Binder "Finite size scaling analysis of ising model block distribution functions", Zeitschrift für Physik B Condensed Matter '''43''' pp. 119-140 (1981)]

Revision as of 18:42, 8 November 2007

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The Binder cumulant for an Ising model with zero field, is given by

where m is the order parameter. In the thermodynamic limit, where the system size , for , and for .

References

  1. K. Binder "Finite size scaling analysis of ising model block distribution functions", Zeitschrift für Physik B Condensed Matter 43 pp. 119-140 (1981)