Constant-pressure Monte Carlo

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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 (Eq. 2 in [1])

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

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_BT \ln \frac{V+\Delta V}{V}\right)\right]

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


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