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&#39;s massive field theory approach is presented.Two-loop calculations and subsequent Padé-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 $Φ(d=3)$, for which we obtain the values $Φ(n=1)\simeq 0.54$ and $Φ(n=0)\simeq 0.52$, considerably lower than the previous $ε$-expansion estimates.