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The crossover region between long-range and short-range interactions for the critical exponents

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arxiv 1407.3358 v1 pith:7X3A67SY submitted 2014-07-12 cond-mat.stat-mech

The crossover region between long-range and short-range interactions for the critical exponents

classification cond-mat.stat-mech
keywords crossoverlong-rangeshort-rangecriticalexponentsregionsystemswell
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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It is well know that systems with an interaction decaying as a power of the distance may have critical exponents that are different from those of short-range systems. The boundary between long-range and short-range is known, however the behavior in the crossover region is not well understood. In this paper we propose a general form for the crossover function and we compute it in a particular limit. We compare our predictions with the results of numerical simulations for two-dimensional long-range percolation.

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Cited by 4 Pith papers

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  2. Matching $A$ with $F$ in long-range QFTs

    hep-th 2026-05 unverdicted novelty 6.0

    In long-range non-unitary φ^4 models the RG flow obeys a gradient structure up to three loops, with A matching the sphere free energy F̃ at leading order.

  3. Matching $A$ with $F$ in long-range QFTs

    hep-th 2026-05 unverdicted novelty 6.0

    RG flow in long-range φ⁴ theories obeys gradient structure ∂_I A = G_IJ β^J up to three loops, with A matching F-tilde and G matching C_IJ at leading nontrivial order.

  4. Matching $A$ with $F$ in long-range QFTs

    hep-th 2026-05 unverdicted novelty 5.0

    Long-range φ⁴ theories have RG beta functions that satisfy a gradient flow with A matching the sphere free energy F̃ at leading nontrivial order.