In high-dimensional critical percolation the rescaled k-point connection probability converges to an explicit constant, confirming the Aizenman-Newman conjecture.
arXiv preprint 2510.03951
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A controlled ε-δ expansion around the LR-SR boundary yields two-loop expressions for ν, η_ω and η_k in long-range quantum O(n) models together with a proposed universality diagram.
A partial reversal of the Simon-Lieb inequality is shown for high-dimensional percolation, implying uniform boundedness of phi_pc(S) and several critical estimates.
citing papers explorer
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Convergence of $k$-point functions in high dimensional percolation
In high-dimensional critical percolation the rescaled k-point connection probability converges to an explicit constant, confirming the Aizenman-Newman conjecture.
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Perturbative Renormalization and Universality Diagram for Long-Range Quantum Criticality
A controlled ε-δ expansion around the LR-SR boundary yields two-loop expressions for ν, η_ω and η_k in long-range quantum O(n) models together with a proposed universality diagram.
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On reversing the Simon-Lieb inequality in high-dimensional percolation
A partial reversal of the Simon-Lieb inequality is shown for high-dimensional percolation, implying uniform boundedness of phi_pc(S) and several critical estimates.