http://debianws.lexgopc.com/wiki143/index.php?action=history&feed=atom&title=User%3AJackliddle%2FMetropolis_algorithmUser:Jackliddle/Metropolis algorithm - Revision history2026-05-08T21:48:59ZRevision history for this page on the wikiMediaWiki 1.43.1http://debianws.lexgopc.com/wiki143/index.php?title=User:Jackliddle/Metropolis_algorithm&diff=961652&oldid=previmported>Jackliddle at 17:50, 26 November 20042004-11-26T17:50:28Z<p></p>
<p><b>New page</b></p><div>The '''Metropolis Algorithm''' is used in the [[Monte Carlo method|Monte Carlo methods]] for [[importance sampling]] probablity distributions.<br />
<br />
The algorithm is widely used in [[lattice gauge theory]].<br />
<br />
==Description== <br />
For generating a sequence of ''[[Field (physics) |field]] configurations'' <math>\Sigma</math> distributed with a probability density <math> e^{-S}</math>. [[Expectation |Expectation values]] of [[Quantum Mechanics| Quantum Mechanical]] [[Observable |observables]] can then be calculated <br />
<br />
<math><O> = \frac{1}{n} \sum_{i=m+1}^{m+n} O(\Sigma_i)</math><br />
<br />
where the first ''m'' steps bring the system into equilbrium.<br />
<br />
If we change one link in the field configuration <math>\Sigma</math> giving us a new configuation <math>\Sigma'</math> there is a corresponding change in the [[action (physics)|action]].<br />
<br />
<math>\Delta S = S(\Sigma') - S(\Sigma)</math><br />
<br />
==Pseudo Code==<br />
using [[Wikipedia:Wikicode|Wikicode]]<br />
<br />
==See also==<br />
*[[Metropolis-Hastings algorithm]]<br />
<br />
<br />
==References==</div>imported>Jackliddle