Binder cumulant - Revision history

Carl McBride: Reverted edits by 70.135.118.126 (talk) to last revision by 134.130.4.242

2012-01-04T14:31:27Z

Reverted edits by 70.135.118.126 (talk) to last revision by 134.130.4.242

← Older revision		Revision as of 16:31, 4 January 2012
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	#[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)]
	[[category: Computer simulation techniques]]		[[category: Computer simulation techniques]]
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	~~[http://thetvtopc.com/Reverse_Cell_Phone_Lookup_Number reverse phone number lookup]~~

70.135.118.126 at 05:56, 4 January 2012

2012-01-04T05:56:58Z

← Older revision		Revision as of 07:56, 4 January 2012
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	#[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)]
	[[category: Computer simulation techniques]]		[[category: Computer simulation techniques]]
			[http://www.prlog.org/11289974-phone-number-lookup-verizon-phone-number-reverse-lookup-to-get-information-you-need-quickly.html phone address lookup]

			[http://thetvtopc.com/Reverse_Cell_Phone_Lookup_Number reverse phone number lookup]

134.130.4.242: (universality class)

2010-06-07T21:59:03Z

(universality class)

← Older revision		Revision as of 23:59, 7 June 2010
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	The '''Binder cumulant''' was introduced by [[Kurt Binder]] in the context of [[Finite size effects \|finite size scaling]]. It is a quantity that ~~is supposed~~ to ~~be invariant for different system sizes at criticality~~. For an [[Ising Models \|Ising model]] with zero field, it is given by		The '''Binder cumulant''' was introduced by [[Kurt Binder]] in the context of [[Finite size effects \|finite size scaling]]. It is a quantity that allows
			to locate the critical point and critical exponents. For an [[Ising Models \|Ising model]] with zero field, it 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]]. It is therefore a fourth order cumulant, related to the kurtosis.		where ''m'' is the [[Order parameters \|order parameter]], i.e. the magnetization. It is therefore a fourth order cumulant, related to the kurtosis.
	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>. Thus, the function is discontinuous in this limit. ~~The useful fact~~ is that ~~curves corresponding to~~ different system sizes ~~(which are, of course, continuous) all intersect at approximately the same [[temperature]]~~, ~~which provides~~ a convenient estimate for the value of the [[Critical points \|critical temperature]].		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>. Thus, the function is discontinuous in this limit. An important observation is that the intersection points of the cumulants for different system sizes usually depend only rather weakly on those sizes, providing a convenient estimate for the value of the [[Critical points \|critical temperature]]. Caution is needed in identifying the universality class from
			the critical value of the Binder cumulant, because that value depends on boundary condition, system shape, and anisotropy of correlations.

	==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)]
	[[category: Computer simulation techniques]]		[[category: Computer simulation techniques]]

Nice and Tidy at 09:56, 13 February 2008

2008-02-13T09:56:45Z

← Older revision		Revision as of 11:56, 13 February 2008
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	==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)]
			[[category: Computer simulation techniques]]

Carl McBride: Slight tidy.

2007-11-12T09:37:42Z

Slight tidy.

← Older revision		Revision as of 11:37, 12 November 2007
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	The '''Binder cumulant''' was introduced by Kurt Binder in the context of finite size scaling. It is a quantity that is supposed to be invariant for different system sizes at criticality. For an [[Ising Models \|Ising model]] with zero field, is given by		The '''Binder cumulant''' was introduced by [[Kurt Binder]] in the context of [[Finite size effects \|finite size scaling]]. It is a quantity that is supposed to be invariant for different system sizes at criticality. For an [[Ising Models \|Ising model]] with zero field, it 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]]. It is therefore a fourth order cumulant, related to the kurtosis.		where ''m'' is the [[Order parameters \|order parameter]]. It is therefore a fourth order cumulant, related to the kurtosis.
			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>. Thus, the function is discontinuous in this limit. The useful fact is that curves corresponding to different system sizes (which are, of course, continuous) all intersect at approximately the same [[temperature]], which provides a convenient estimate for the value of the [[Critical points \|critical temperature]].
	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>. Thus, the function is discontinuous in this limit ~~--- the~~ useful fact is that curves corresponding to different system sizes (which are, of course, continuous) all intersect at approximately the same temperature, which provides a convenient ~~estimatation~~ of the critical temperature.

	==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)]

Dduque at 21:36, 8 November 2007

2007-11-08T21:36:51Z

← Older revision		Revision as of 23:36, 8 November 2007
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	~~{{Stub-general}}~~		The '''Binder cumulant''' was introduced by Kurt Binder in the context of finite size scaling. It is a quantity that is supposed to be invariant for different system sizes at criticality. 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]].		where ''m'' is the [[Order parameters \|order parameter]]. It is therefore a fourth order cumulant, related to the kurtosis.
	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>. Thus, the function is discontinuous in this limit --- the useful fact is that curves corresponding to different system sizes (which are, of course, continuous) all intersect at approximately the same temperature, which provides a convenient estimatation of the critical temperature.

	==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)]

Carl McBride at 17:42, 8 November 2007

2007-11-08T17:42:47Z

← Older revision		Revision as of 19:42, 8 November 2007
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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)]

Carl McBride: New page: {{Stub-general}} The '''Binder cumulant''' for an Ising model with zero field, is given by : $U_4 = 1- \frac{\langle m^4 \rangle }{3\langle m^2 \rangle^2 }$ . ...

2007-11-08T17:41:34Z

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> . ...

New page

{{Stub-general}}
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> .

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==
#[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)]