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

TL;DR

This paper investigates the crossover between long-range and short-range interactions in critical phenomena, proposing a general crossover function and validating it through numerical simulations in 2D long-range percolation.

Contribution

It introduces a general form for the crossover function and computes it analytically, enhancing understanding of the transition between interaction regimes.

Findings

Proposed a universal crossover function for critical exponents.

Validated the theoretical predictions with numerical simulations.

Identified the behavior of critical exponents in the crossover region.

Abstract

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.