In a Monte Carlo calculation by the Metropolis method, a trial move of an atom raises the energy of the system by 0.10 eV. At a temperature of 1000 K, which is closest to the probability of accepting this move? Take k = 8.617×10⁻⁵ eV/K.

Answer: C. About 0.31

In the Metropolis method, moves that lower the energy are always accepted, and moves that raise it are accepted with probability exp(−ΔE/kT). Since kT = 8.617×10⁻⁵ × 1000 ≈ 0.0862 eV, ΔE/kT ≈ 1.16, and the probability is exp(−1.16) ≈ 0.31. In practice a random number between 0 and 1 is generated, and the move is accepted if it is smaller than this probability. By accepting energy-raising moves with a certain probability, the system visits states following the Boltzmann distribution, and averages give the equilibrium properties at finite temperature. If energy-raising moves were never accepted, the system would be trapped in a local energy minimum, the same as optimization at 0 K. About 0.69 mistakes the rejection probability 1 − 0.31 for the acceptance probability.