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math-ph2021
Mean-field behavior of nearest-neighbor oriented percolation on the BCC lattice above dimensions
Lung-Chi Chen, Satoshi Handa, Yoshinori Kamijima
In this paper, we consider nearest-neighbor oriented percolation with independent Bernoulli bond-occupation probability on the -dimensional body-centered cubic (BCC) lattice $\m…
math-ph2021★ 1 cited
Long-Range Ising Models: Contours, Phase Transitions and Decaying Fields
Lucas Affonso, Rodrigo Bissacot, Eric O. Endo +1
Inspired by Fröhlich-Spencer and subsequent authors who introduced the notion of contour for long-range systems, we provide a definition of contour and a direct proof for the phase…
math-ph2016
Mean-field bound on the 1-arm exponent for Ising ferromagnets in high dimensions
Satoshi Handa, Markus Heydenreich, Akira Sakai
The 1-arm exponent for the ferromagnetic Ising model on is the critical exponent that describes how fast the critical 1-spin expectation at the center of the bal…