Constant-pressure Monte Carlo

In constant-pressure Monte Carlo a trial change in the volume becomes one of the Monte Carlo moves. The weighting function, w, is given by (Ref 1 Eq. 2)

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for a change in volume, $\Delta V$, one has

$r={\frac {w_{\rm {new}}}{w_{\rm {old}}}}=\exp \left[-\beta \left(\Delta U+p\Delta V-Nk_{B}T\ln {\frac {V+\Delta V}{V}}\right)\right]$

If $r\geq 1$ then the move is accepted, and if $0<r<1$ then r is compared with a random number $0<x<1$. If 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 x \le r} then the move is accepted.

References

1. R. Eppenga and D. Frenkel "Monte Carlo study of the isotropic and nematic phases of infinitely thin hard platelets", Molecular Physics 52 pp. 1303-1334 (1984)