November 12 2003

Test run for Albert's algorithm

An S_50_50_100 system have been cooled down slowly from T=0.0095 to T=0.0055. Then the last equilibrated configurations for both solid (T=0.0055) and liquid(T=0.0095) seperately have been gone through basic MC algorithm and the Albert's algorithm with external electric field set to 0. The total runs have 100 passes (250000 steps) and the first 10 passes have been discarded.

For each method 10 individual runs have been performed. The average values and the standard deviations of average potential energy <E> have been calculated to compare these two methods. In the Albert's algorithm, <E> has also been calculated by the random sampling method.

In the following table the values of <E> - E0 (E0 is the potential energy of the initial configuration) are listed.

Results for <E>

E0 MC Albert's Sampling
Solid -2.0997107500e+04 (2.76 +/- 2.57)*10E-4 (10.07 +/- 6.40)*10E-4 (10.06 +/- 6.57)*10E-4
Liquid -2.0996121740e+04 (-4.76 +/- 0.91)*10E-2 (-3.45 +/- 0.51)*10E-2 (-3.52 +/- 0.59)*10E-2

From the table we can see, regardless the bad statistical errors due to the short running time, the results from Albert's algorithm agree with those from basic MC. The random sampling method is pretty good with sampling average values.