Random currents and sharpness

The random-current representation of Ising correlations and the switching lemma, and the sharpness of the Ising phase transition: the Simon–Lieb inequality, exponential decay of correlations below the critical point and the mean-field lower bound on the magnetization above it.

• Random currents and the switching lemma
• Simon–Lieb inequality
• Sharpness of the phase transition for the Ising model
• Mean-field lower bound for the Ising magnetization

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