Spin-glass with long-range random exchange interaction

Abstract

We consider the spin-glass (SG) with long-range (LR) random exchange interaction varying with distance $R$ as ${R}^{\ensuremath{-}\frac{d}{2}\ensuremath{-}\frac{\ensuremath{\sigma}}{2}}$, where $d$ is the space dimensionality and $\ensuremath{\sigma}>0$. It is shown that the LR fixed point is stable if $\ensuremath{\sigma}<2$. The nonclassical ($d<3\ensuremath{\sigma}$) LR critical exponents in powers of $3\ensuremath{\sigma}\ensuremath{-}d$ are not continuous at $\ensuremath{\sigma}=2$ when the transition to short-range (SR) exchange is made.