Metropolis Monte Carlo

Metropolis Monte Carlo (MMC)

MMC Simulations can be carried out in different ensembles. For the case of one-component systems the usual ensembles are:

• Canonical ensemble (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NVT } )

• Isothermal-Isobaric ensemble (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NpT } )

• Grand canonical ensemble (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu V T } )

The purpose of these techniques is to sample representative configurations of the system at the corresponding thermodynamic conditions.

The samplinng techniques make use the so-called pseudo- random number generators

Temperature

The temperature is usually fixed in MMC simulations, since in clasical statistics the kinetic degrees of freedom (momenta) can be generally, integrated out.

However, it is possible to design procedures to perform MMC simulations in the microcanonic ensembe (NVE).

References

M.P. Allen and D.J. Tildesley , etc