Surface critical behavior in fixed dimensions d

Abstract

The critical behavior of semi-infinite systems in fixed dimensions $d<4$ is investigated theoretically. The appropriate extension of Parisi's massive field theory approach is presented. Two-loop calculations and subsequent Pad\'e-Borel analyses of surface critical exponents of the special and ordinary phase transitions yield estimates in reasonable agreement with recent Monte Carlo results. This includes the crossover exponent $\ensuremath{\Phi}(d=3)$, for which we obtain the values $\ensuremath{\Phi}(n=1)\ensuremath{\simeq}0.54$ and $\ensuremath{\Phi}(n=0)\ensuremath{\simeq}0.52$, considerably lower than the previous $\ensuremath{\epsilon}$-expansion estimates.