1999/12/20 by X. S. Chen, X.S. Chen, V. Dohm · 2 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s100510051127
LaTex, 59 pages, accepted for publication in Eur. Phys. J.B
arxiv created 1999/12/20 · openalex publication_date 2000/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study the large-r behavior of the bulk order-parameter correlation function G(\bfr) for T>Tc within the lattice ϕ4 theory. We also study the large-L behavior of the susceptibility χ of the confined lattice system of size L with periodic boundary conditions. The large-L behavior of χ is closely related to the large-r behavior of G(\bfr). Explicit results are derived for d>2. Finite-size scaling must be formulated in terms of the anisotropic exponential correlation length ξ1 that governs the decay of G(\bfr) for large r rather than in terms of the isotropic correlation length ξ defined via the second moment of G(\bfr). This result modifies a recent interpretation concerning an apparent violation of finite-size scaling in terms of ξ≠ ξ1. Exact results for the d=1 Ising model illustrate our conclusions. Furthermore, we show that the exponential finite-size behavior for L/ξ≫ 1 is not captured by the standard perturbation approach that separates the lowest mode from the higher modes. Consequences for the theory of finite-size effects for d>4 are discussed. The two-variable finite-size scaling form predicts an approach ∝ e-L/ξ1 to the bulk critical behavior whereas a single-variable scaling form implies a power-law approach ∝ L-d.