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Critical Behavior of the Nonlinear σ\sigma Model With a Free Surface: The 'Ordinary' Transition in (2+epsilon)-dimensions

1986
4 pages
Published in:
  • Phys.Rev.Lett. 56 (1986) 2834-2837
DOI:
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Abstract: (APS)
We analyze the critical behavior of isotropic ferromagnets with a free surface by means of field-theoretic renormalization methods in d=2+ε dimensions. Renormalization-group equations for surface quantities are derived which imply scaling to all orders in ε. Explicit results to order ε2 are presented for the critical surface exponents of the ordinary transition. Interpolation with the known results near four dimensions yields estimates for d=3 which seem to be remarkably accurate.
  • MODEL: FERROMAGNET
  • FIELD THEORETICAL MODEL: SIGMA
  • NONLINEAR
  • FIELD THEORY: TWO-DIMENSIONAL
  • FIELD THEORY: CRITICAL PHENOMENA
  • APPROXIMATION: EPSILON EXPANSION
  • SCALING
  • RENORMALIZATION GROUP
  • STATISTICAL MECHANICS: THREE-DIMENSIONAL
  • APPROXIMATION: PADE
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