The linear Ising model and its analytic continuation, random walk

Details The linear Ising model and its analytic continuation, random walk The linear Ising model and its analytic continuation, random walk

2004-02-24

arxiv.org/abs/cond-mat/0402600v1

Nuovo Cimento B 119 (2004) 181-189

Physics

Condensed Matter

Statistical Mechanics

5 pages

Scientific paper

10.1393/ncb/i2004-10061-6

A generalization of Gauss's principle is used to derive the error laws corresponding to Types II and VII distributions in Pearson's classification scheme. Student's $r$-pdf (Type II) governs the distribution of the internal energy of a uniform, linear chain, Ising model, while analytic continuation of the uniform exchange energy converts it into a Student $t$-density (Type VII) for the position of a random walk in a single spatial dimension. Higher dimensional spaces, corresponding to larger degrees of freedom and generalizations to multidimensional Student $r$- and $t$-densities, are obtained by considering independent and identically distributed random variables, having rotationally invariant densities, whose entropies are additive and generating functions are multiplicative.

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