Surface critical behavior in fixed dimensions $d<4$: Nonanalyticity of critical surface enhancement and massive field theory approach

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 $\Phi (d=3)$, for which we obtain the values $\Phi (n=1)\simeq 0.54$ and $\Phi (n=0)\simeq 0.52$, considerably lower than the previous $\epsilon$-expansion estimates.