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The crossover region between long-range and short-range interactions for the critical exponents. (English) Zbl 1318.82017
It 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.

MSC:
82B27 Critical phenomena in equilibrium statistical mechanics
82B43 Percolation
82D40 Statistical mechanics of magnetic materials
05C83 Graph minors
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