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arXiv · 2412.07098

Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours

Lucas Affonso·Rodrigo Bissacot·Henrique Corsini·Kelvyn Welsch
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Abstract

Following seminal work by J. Fr\"ohlich and T. Spencer on the critical exponent $\alpha=2$, we give a proof via contours of phase transition in the one-dimensional long-range ferromagnetic Ising model in the entire region of decay, where phase transition is known to occur, i.e., polynomial decay $\alpha \in (1,2]$. No assumptions that the nearest-neighbor interaction $J(1)$ is large are made. The robustness of the method also yields a proof of phase transition in the presence of a nonsummable external field that decays sufficiently fast.

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Lucas Affonso, Rodrigo Bissacot, Henrique Corsini, Kelvyn Welsch. 2024-12-10. Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours. https://arxiv.org/abs/2412.07098

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