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

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arxiv 2412.07098 v2 pith:XIWLK5NV submitted 2024-12-10 math-ph cond-mat.stat-mechmath.MPmath.PR

classification math-phcond-mat.stat-mechmath.MPmath.PR
keywords phaseprooftransitionalphacontoursdecayisinglong-range
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Phase transitions in low-dimensional long-range random field Ising models

    math.PR 2024-12 conditional novelty 8.0 of 10

    Phase transitions occur in the long-range RFIM in d=1 for 1<α<3/2 and in d=2 for 2<α≤3, including the critical α=3.

  2. A Cluster Expansion and the Decay of Correlations of the 1D Long-Range Ising Model at Low Temperatures

    math-ph 2026-02 conditional novelty 7.0 of 10

    For the 1D long-range ferromagnetic Ising model with J(r)=r^{-α} (1<α≤2), a convergent low-temperature cluster expansion is established and the two-point truncated correlation is shown to decay with the exact algebrai...

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