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

*(English)*Zbl 1318.82017It is well known 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. There is a value of the exponent that separates the short-range behavior from the long-range behavior. The following natural question is interesting: What happens at this crossover point? In this paper, the authors propose a general form for the crossover function. Namely, they find that there is a non-trivial behavior at the crossover point, i.e., one has logarithmic correlations to the standard power law behavior. They compare the obtained predictions with the results of numerical simulations for two-dimensional long-range percolation.

Reviewer: Farruh Mukhamedov (Kuantan)

##### MSC:

82B27 | Critical phenomena in equilibrium statistical mechanics |

82B43 | Percolation |

82D40 | Statistical mechanics of magnetic materials |

05C83 | Graph minors |

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\textit{E. Brezin} et al., J. Stat. Phys. 157, No. 4--5, 855--868 (2014; Zbl 1318.82017)

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