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)

$w\simeq c{\frac {V^{N}}{N!}}\exp \left[-\beta (U(q^{N}))+pV\right]$

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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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 $x\leq r$ 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)