Moments and distribution functions for polymers using Toeplitz matrices

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Abstract
A method is given for calculating the moments and distribution functions for the finite one dimensional Ising model. With the technique presented, as many as 20 or so moments can be calculated as explicit matrix products, thus avoiding the use of numerical differentiation. Previously it was feasible to calculate only the first two moments (giving the mean value and dispersion of the distribution). Using short polypeptide chains as an example where the distribution function is known, it is shown that knowledge of a large number of moments allows very broad, non−Gaussian distributions with more than one maximum to be accurately determined.