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arXiv · 1808.00439

Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature

Hugo Duminil-Copin·Subhajit Goswami·Aran Raoufi
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Abstract

The truncated two-point function of the ferromagnetic Ising model on $\mathbb Z^d$ ($d\ge3$) in its pure phases is proven to decay exponentially fast throughout the ordered regime ($\beta>\beta_c$ and $h=0$). Together with the previously known results, this implies that the exponential clustering property holds throughout the model's phase diagram except for the critical point: $(\beta,h) = (\beta_c,0)$.

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Hugo Duminil-Copin, Subhajit Goswami, Aran Raoufi. 2018-08-01. Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature. https://doi.org/10.1007/s00220-019-03633-y

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