Computational Physics

References 335

Metropolis method, in which creations are tried much more often than annihilations.

Suppose the trial probabilities for creation and annihilation arePCandPA

respectively.

Show that the acceptances should be modified as follows:

• The acceptance probability for creation is
  Pacc=min(1,qXX′)
  with
  qXX′=e−βU

+

−^3 V/(N+ 1 )eβμ

PA

PC

• Similarly for annihilation:
  Pacc=min(1,qXX′)
  with
  qXX′=eβU
  −
  ^3 N/Ve−βμ

PC

PA

Show that this modification can be implemented by a suitable shift in the chemical
potential. Find this shift.
10.4 [C] Consider the methane (CH 4 ) molecule of Problem 8.12. In that problem we have
given the potential energy of the molecule in terms of stretching and bending terms.
Write a Monte Carlo simulation for simulating this molecule at a given temperature.
Compare the results with those obtained in Problem 8.12.

References

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[3] K. Binder, ed.,Applications of the Monte Carlo Method in Statistical Physics,Topics in Current
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[5] M. H. Kalos and P. A. Whitlock,Monte Carlo Methods. New York, John Wiley, 1986.
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Springer, 1988.
[7] G. T. Barkema and M. E. J. Newman,Monte Carlo Methods in Statistical Physics. Oxford,
Oxford University Press, 1999.
[8] D. Frenkel,Monte Carlo Simulations. Utrecht, Van ’t Hoff laboratory, University of Utrecht,
The Netherlands, 1988.
[9] F. James, ‘Monte Carlo theory and practice,’Rep. Prog. Phys., 43 (1980), 1145–89.
[10] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, ‘Equation of
state calculations by fast computing machines,’J. Chem. Phys., 21 (1953), 1087–92.
[11] W. W. Wood and J. D. Jacobsen, ‘Monte Carlo calculations in statistical mechanics,’Proceed-
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