# Long-range critical exponents near the short-range crossover

## TL;DR

This paper introduces a new weakly coupled field-theoretic description for the long-range Ising model near the short-range crossover, enabling the calculation of critical exponents and revealing an infrared duality.

## Contribution

It presents a novel weakly coupled framework for analyzing the long-range to short-range crossover in the Ising model, contrasting with the traditional strongly coupled approach.

## Key findings

- Derived critical exponents near the crossover point.
- Identified an infrared duality between two UV descriptions.
- Provided a new computational method for long-range critical phenomena.

## Abstract

The $d$-dimensional long-range Ising model, defined by spin-spin interactions decaying with the distance as the power $1/r^{d+s}$, admits a second order phase transition with continuously varying critical exponents. At $s = s_*$, the phase transition crosses over to the usual short-range universality class. The standard field-theoretic description of this family of models is strongly coupled at the crossover. We find a new description, which is instead weakly coupled near the crossover, and use it to compute critical exponents. The existence of two complementary UV descriptions of the same long-range fixed point provides a novel example of infrared duality.