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The Wulff crystal of self-dual FK-percolation becomes round when approaching criticality

Ioan Manolescu, Maran Mohanarangan

17/3/26 Published in : arXiv:2603.16318

The study of the phase transition in planar FK-percolation on the square lattice has seen significant recent breakthroughs. The model undergoes a change in the nature of its phase transition at q = 4, transitioning from a continuous to a discontinuous regime. The aim of this article is to investigate the behaviour of the model in the discontinuous regime as q > 4 approaches the continuous transition point 4 from above, while maintaining the critical parameter p = p_c(q). We prove that in this limit, the correlation length becomes isotropic. The core of the proof builds upon the recently established rotational invariance of the large-scale features of the model at q = 4 (arXiv:2012.11672).

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Phase I & II research project(s)

  • Statistical Mechanics

Phase III direction(s)

  • Statistical Mechanics and Random Structures
  • Spectral gap problems in non-perturbative quantum theory

Gaussian free field convergence of the six-vertex model with -1\leqΔ\leq-\frac12

Cosmology and modified GW propagation from the BNS mass function at third-generation detector networks

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