Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0

Abstract

We simulate self-avoiding walks on a cubic lattice and determine the second virial coefficient for walks of different lengths. This allows us to determine the critical value of the renormalized four-point coupling constant in the three-dimensional N-vector universality class for N=0. We obtain g* = 1.4005(5), where g is normalized so that the three-dimensional field-theoretical beta-function behaves as β(g) = - g + g^2 for small g. As a byproduct, we also obtain precise estimates of the interpenetration ratio Psi*, Psi* = 0.24685(11), and of the exponent ν, ν= 0.5876(2).

16 pages

References in corpus (20)

• Critical Phenomena and Renormalization-Group Theory
• Critical Exponents of the N-vector model
• Critical exponents and equation of state of the three-dimensional Heisenberg universality class
• Critical behavior of the three-dimensional XY universality class
• Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks
• The critical exponents of the superfluid transition in He4
• 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
• Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point
• Scaling of Star Polymers with one to 80 Arms
• Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
• High-precision determination of the critical exponent gamma for self-avoiding walks
• High Precision Measurement of the Thermal Exponent for the Three-Dimensional XY Universality Class
• Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices
• Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model
• Scaling of Self-Avoiding Walks and Self-Avoiding Trails in Three Dimensions
• Virial coefficients and osmotic pressure in polymer solutions in good-solvent conditions
• Static Scaling Behavior of High-Molecular-Weight Polymers in Dilute Solution: A Reexamination
• The effective potential of N-vector models: a field-theoretic study to O(ε^3)
• Dynamic critical behavior of the Swendsen--Wang Algorithm for the three-dimensional Ising model
• Polymer size in dilute solutions in the good-solvent regime

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• Two-parameter model predictions and theta-point crossover for linear-polymer solutions
• Effective average action based approach to correlation functions at finite momenta
• Phi4tools: Compilation of Feynman diagrams for Landau-Ginzburg-Wilson theories