Mass Scaling of the Near-Critical 2D Ising Model Using Random Currents
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Mass Scaling of the Near-Critical 2D Ising Model Using Random Currents. / Klausen, Frederik Ravn; Raoufi, Aran.
In: Journal of Statistical Physics, Vol. 188, No. 3, 21, 2022, p. 1-21.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Mass Scaling of the Near-Critical 2D Ising Model Using Random Currents
AU - Klausen, Frederik Ravn
AU - Raoufi, Aran
PY - 2022
Y1 - 2022
N2 - We examine the Ising model at its critical temperature with an external magnetic field ha158 on aZ2 for a,h>0. A new proof of exponential decay of the truncated two-point correlation functions is presented. It is proven that the mass (inverse correlation length) is of the order of h815 in the limit h→0. This was previously proven with CLE-methods in Camia et al. in (Commun Pure Appl Math 73(7):1371–405, 2020). Our new proof uses instead the random current representation of the Ising model and its backbone exploration. The method further relies on recent couplings to the random cluster model (Aizenman et al. in Invent Math 216:661–743, 2018) as well as a near-critical RSW-result for the random cluster model (Duminil-Copin and Manolescu in Planar Random-Cluster Model: Scaling Relations, 2020).
AB - We examine the Ising model at its critical temperature with an external magnetic field ha158 on aZ2 for a,h>0. A new proof of exponential decay of the truncated two-point correlation functions is presented. It is proven that the mass (inverse correlation length) is of the order of h815 in the limit h→0. This was previously proven with CLE-methods in Camia et al. in (Commun Pure Appl Math 73(7):1371–405, 2020). Our new proof uses instead the random current representation of the Ising model and its backbone exploration. The method further relies on recent couplings to the random cluster model (Aizenman et al. in Invent Math 216:661–743, 2018) as well as a near-critical RSW-result for the random cluster model (Duminil-Copin and Manolescu in Planar Random-Cluster Model: Scaling Relations, 2020).
U2 - 10.1007/s10955-022-02939-x
DO - 10.1007/s10955-022-02939-x
M3 - Journal article
VL - 188
SP - 1
EP - 21
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 3
M1 - 21
ER -
ID: 318817519