1998/04/07 by H. W. Diehl, M. A. Shpot, M. Shpot · 122 citations
Mathematics · Physics and Astronomy · #Coupling constant #Critical exponent #Critical phenomena #Exponent #Geometry #Inverse #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Renormalization #Renormalization group #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1016/s0550-3213(98)00489-1
published in Nuclear Physics B 528(3), 595-647 (Elsevier BV) · Revtex, 40 pages, 3 figures, and 8 pictograms (included in equations)
arxiv created 1998/04/07 · openalex publication_date 1998/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 having to resort to the ε expansion. The approach is elaborated for the representative case of the semi-infinite |\bboxϕ|4 n-vector model with a boundary term 1/2 c0∫∂ V\bboxϕ2 in the action. To make the theory uv finite in bulk dimensions 3≤ d<4, a renormalization of the surface enhancement c0 is required in addition to the standard mass renormalization. Adequate normalization conditions for the renormalized theory are given. This theory involves two mass parameter: the usual bulk `mass' (inverse correlation length) m, and the renormalized surface enhancement c. Thus the surface renormalization factors depend on the renormalized coupling constant u and the ratio c/m. The special and ordinary surface transitions correspond to the limits m→ 0 with c/m→ 0 and c/m→∞, respectively. It is shown that the surface-enhancement renormalization turns into an additive renormalization in the limit c/m→∞. The renormalization factors and exponent functions with c/m=0 and c/m=∞ that are needed to determine the surface critical exponents of the special and ordinary transitions are calculated to two-loop order. The associated series expansions are analyzed by Padé-Borel summation techniques. The resulting numerical estimates for the surface critical exponents are in good agreement with recent Monte Carlo simulations. This also holds for the surface crossover exponent Φ.