Analysis of experimental specific heat data near the critical temperature. I. Theory

The problem of determining the critical parameters of the specific heat of a ferromagnet or antiferromagnet is discussed. A method is developed based on fitting the data by least-squares-cubic splines with variable knots. The fitted function is then differentiated, thus reducing by one the number of critical parameters. The critical temperature is estimated by a linearity conditions, which is justified mathematically. This further reduces the number of critical parameters. The method is illustrated for some test data specifically chosen to simulate realistic data, and is shown to work well provided the signal-to-noise ratio of the data is better than 20:1.