Abstract
The random walk representation of then-dimensional Ising model exhibits the 2-point correlation function 〈σ(x) σ(y)〉 as a sum of positive contributions of paths ω fromx toy. We derive upper bounds on the individual terms in this sum for low temperatures. Each term tends to zero as β → ∞, while the correlation function itself tends to 1. Therefore increasingly more and longer paths contribute when β is lowered.
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Communicated by G. Mack
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Maren, T.R. Probability distribution of random paths in the Ising model at low temperature. Commun.Math. Phys. 88, 105–112 (1983). https://doi.org/10.1007/BF01206882
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DOI: https://doi.org/10.1007/BF01206882