98-07E

98-07E

By - Posted on 08 February 2012

UDC:
536.425.764; 538.221
PACS:
64.60.Ht, 68.35.Rh, 05.40.+j, 11.10.-7

Surface critical behavior in semi-infinite systems: massive field theory approach

H.W. Diehl
M. Shpot

The massive field-theory approach for studying critical behavior in fixed space dimensions $d<4$ is extended to systems with surfaces. This enables one to study surface critical behavior directly in dimensions $d<4$ without resorting to the $\epsilon$ expansion. Two-loop calculations are presented for the case of the semi-infinite $|{\phi }|^4$ $n$-vector model with a boundary term $\propto \intop \nolimits _{\partial V}{\phi }^2$ in $d=3$ bulk dimensions. Both the special and ordinary phase transitions are investigated. The Pad\'e-Borel analysis of the resulting renormalized perturbation expansions yields numerical estimates of surface critical exponents in reasonable agreement with the most recent experimental work and Monte Carlo simulations. This includes the surface crossover exponent $\Phi$, for which we obtain the values $\Phi (n\mskip -\thinmuskip =\mskip -\thinmuskip 0)\simeq 0.52$ and $\Phi (n\mskip -\thinmuskip =\mskip -\thinmuskip 1)\simeq 0.54$ considerably lower than the previous $\epsilon$-expansion estimates.

Year:
1998
Pages:
49