Statistical and Systematic Errors

The statistical error in the fitted critical exponent is easily estimated from the least squares fitting procedure. Systematic errors are more difficult to take into account. In this work an attempt is made to consider 3 sources of systematic error:

• Limited range of system sizes: has been considered and the effect of ignoring the smaller system sizes tested.
• Width of the critical region: the maximum range of disorder is imposed by but may still be too large. The effect of narrowing this range still further has been tested.
• The choice of distribution of random numbers: this has been tested by comparing the rectangular and Gaussian cases.

These tests are represented in figure 2. Unfortunately the general increase in the error bars due to ignoring data tends to mask any systematic changes. There does however appear to be a general increase in the exponents when the data is eliminated and a tendency for the Gaussian data to lie below the rectangular. From this data has been estimated, where the error bar may be somewhat wider than necessary.