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

TL;DR

This paper extends massive field theory to analyze surface critical behavior in systems with dimensions less than four, providing estimates for surface exponents that align with Monte Carlo results and differ from previous epsilon-expansion estimates.

Contribution

It introduces an extension of Parisi's massive field theory approach for fixed dimensions below four to study surface critical phenomena.

Findings

Surface critical exponents estimated with two-loop calculations.

Results agree with recent Monte Carlo simulations.

Crossover exponent values are lower than previous epsilon-expansion estimates.

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.