Critical behavior ofm-component magnets with correlated impurities

摘要: We study the critical behavior of an $m$-component classical spin system with quenched impurities correlated along ${\ensuremath{\epsilon}}_{d}$-dimensional "line" and randomly distributed in $d\ensuremath{-}{\ensuremath{\epsilon}}_{d}$ dimensions ($d=4\ensuremath{-}\ensuremath{\epsilon}$). The presence this line makes anisotropic interactions highly nonlocal. renormalization group (RG) is used to approach region quantities interest are calculated a double $\ensuremath{\epsilon}$, ${\ensuremath{\epsilon}}_{d}$ expansion. A two-loop calculation needed expose fully divergent structure, theory proved be renormalizable up order. consequence expansion fact that RG functions consequently exponents depend on ratio $\frac{{\ensuremath{\epsilon}}_{d}}{(\ensuremath{\epsilon}+{\ensuremath{\epsilon}}_{d})}$. solution equations leads existence two correlation lengths: parallel perpendicular it, ${\ensuremath{\nu}}_{\ensuremath{\parallel}}$ ${\ensuremath{\nu}}_{\ensuremath{\perp}}$, respectively, relation ${\ensuremath{\nu}}_{\ensuremath{\parallel}}=z{\ensuremath{\nu}}_{\ensuremath{\perp}}$. exponent $z$ results from anisotropy system. New scaling laws found for exponents: $\ensuremath{\gamma}={\ensuremath{\nu}}_{\ensuremath{\perp}}(2\ensuremath{-}\ensuremath{\eta})$ $\ensuremath{\alpha}=2\ensuremath{-}(d\ensuremath{-}{\ensuremath{\epsilon}}_{d}){\ensuremath{\nu}}_{\ensuremath{\perp}}\ensuremath{-}{\ensuremath{\epsilon}}_{d}{\ensuremath{\nu}}_{\ensuremath{\parallel}}$. establish between our model quantum one less dimension random pointlike impurities. For we predict quantum-to-classical crossover at finite temperature cross-over ${\ensuremath{\nu}}_{\ensuremath{\parallel}}^{\ensuremath{-}1}$.