Sharp Asymptotics for the Truncated Two-Point Function of the Ising Model with a Positive Field

Abstract

We prove that the correction to exponential decay of the truncated two points function in the homogeneous positive field Ising model is $c\Vert x{\Vert }^{-(d-1)/2}$. The proof is based on the development in the random current representation of a "modern" Ornstein-Zernike theory, as developed by Campanino, Ioffe and Velenik.

26 pages, 7 figures, details added

References in corpus (4)

• Fluctuation theory of connectivities for subcritical random cluster models
• Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature
• Potts models with a defect line
• Asymptotics of even-even correlations in the Ising model

Cited by in corpus (5)

• Asymptotics of even-even correlations in the Ising model
• On the two-point function of the Potts model in the saturation regime
• Non-analyticity of the correlation length in systems with exponentially decaying interactions
• Failure of Ornstein--Zernike asymptotics for the pair correlation function at high temperature and small density
• Ornstein-Zernike behavior for Ising models with infinite-range interactions