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- W4313202046 abstract "We consider the Random-Cluster model on $mathbb{Z}^d$ with interactions of infinite range of the form $J_x = psi(x)mathsf{e}^{-rho(x)}$ with $rho$ a norm on $mathbb{Z}^d$ and $psi$ a subexponential correction. We first provide an optimal criterion ensuring the existence of a nontrivial saturation regime (that is, the existence of $beta_{rm sat}(s)>0$ such that the inverse correlation length in the direction $s$ is constant on $[0,beta_{rm sat}(s))$), thus removing a regularity assumption used in a previous work of ours. Then, under suitable assumptions, we derive sharp asymptotics (which are not of Ornstein-Zernike form) for the two-point function in the whole saturation regime $(0,beta_{rm sat}(s))$. We also obtain a number of additional results for this class of models, including sharpness of the phase transition, mixing above the critical temperature and the strict monotonicity of the inverse correlation length in $beta$ in the regime $(beta_{rm sat}(s), beta_{rm c})$." @default.
- W4313202046 created "2023-01-06" @default.
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- W4313202046 date "2022-12-25" @default.
- W4313202046 modified "2023-10-01" @default.
- W4313202046 title "On the Two-Point Function of the Potts Model in the Saturation Regime" @default.
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- W4313202046 doi "https://doi.org/10.1007/s00220-022-04574-9" @default.
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