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• W2750863630 abstract "We consider the Ising model at its critical temperature with external magnetic field $ha^{15/8}$ on $amathbb{Z}^2$. We give a purely probabilistic proof, using FK methods rather than reflection positivity, that for $a=1$, the correlation length is $geq const.~h^{-8/15}$ as $hdownarrow0$. We extend to the $adownarrow0$ continuum limit the FK-Ising coupling for all $h>0$, and obtain tail estimates for the largest renormalized cluster area in a finite domain as well as an upper bound with exponent $1/8$ for the one-arm event. Finally, we show that for $a=1$, the average magnetization, $mathcal{M}(h)$, in $mathbb{Z}^2$ satisfies $mathcal{M}(h)/h^{1/15}rightarrow$ some $Bin(0,infty)$ as $hdownarrow0$." @default.
• W2750863630 created "2017-09-15" @default.
• W2750863630 creator A5029447271 @default.
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• W2750863630 date "2017-09-02" @default.
• W2750863630 modified "2023-09-27" @default.
• W2750863630 title "FK-Ising coupling applied to near-critical planar models" @default.
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• W2750863630 hasPublicationYear "2017" @default.
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