Domain of computation of a random field in statistical physics (1995) [12 citations — 7 self]
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@INPROCEEDINGS{Edalat95domainof,author = {Abbas Edalat},
title = {Domain of computation of a random field in statistical physics},
booktitle = {Theory and Formal Methods 1994: Proceedings of the second Imperial College Department of Computing Workshop on Theory and Formal Methods},
year = {1995},
pages = {11--14},
publisher = {IC Press}
}
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Abstract:
We present a domain-theoretic analysis of the invariant measure of the one-dimensional Ising model in a random external magnetic field. The invariant measure is obtained as a fixed point of the Markov transition operator of an iterated function system with probabilities acting on the probabilistic power domain of the upper space of a closed real interval. This enables us to use the generalised Riemann integral in combination with Elton's ergodic theorem to obtain an algorithm to compute the free energy density of the system. We also develop the generalised double Riemann integral, which we use, together with a two-dimensional version of Elton's theorem, to deduce algorithms to compute the magnetisation per spin and the Edwards-Anderson parameter of the system. 1
