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Critical behavior of the Ising model with long range interactions

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arxiv 1207.1018 v1 pith:VDEF3XNJ submitted 2012-07-04 cond-mat.stat-mech hep-th

Marco Picco (LPTHE) This is my paper
classification cond-mat.stat-mechhep-th
keywords rangemodelinteractionsisinglargelongresultsagree
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abstract

We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter $\sigma$ and for large sizes. We observe that the results close to the change of regime from intermediate to short range do not agree with the renormalization group predictions.

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Cited by 3 Pith papers

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  1. Critical long-range percolation II: Low effective dimension

    math.PR 2025-08 conditional novelty 8.0 of 10

    In the long-range low-dimensional regime of percolation, the cluster volume tail and k-point functions are determined up to constants, yielding the hyperscaling identities delta=(d+alpha)/(d-alpha) and d_f=(d+alpha)/2.

  2. Spontaneous Symmetry Breaking in Two-dimensional Long-range Heisenberg Model

    cond-mat.stat-mech 2025-12 conditional novelty 7.0 of 10

    The 2D long-range Heisenberg model has a finite-temperature transition and long-range order for σ ≤ 2, with logarithmic corrections at σ=2.

  3. Long range to short range crossover in one dimension

    cond-mat.stat-mech 2025-07 conditional novelty 5.0 of 10

    A 1D self-avoiding Levy-flight simulation supports Sak's LR-to-SR crossover at sigma*=1, with long-range exponents close to, but distinct from, Flory predictions.

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