Long-range critical exponents near the short-range crossover
Connor Behan, Leonardo Rastelli, Slava Rychkov, Bernardo Zan
TL;DR
The existence of two complementary UV descriptions of the same long-range fixed point provides a novel example of infrared duality.
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.