An Asymptotic Formula for Marginal Running Coupling Constants and Universality of loglog Corrections∗

if a real solution a∗ for a∗ + V (a∗) = 0 (3) exists and g(t) starts from an appropriate neighborhood of a∗. The leading term is universal in the sense that an initial data does not appear in this term. The purpose of this work is (i) to find a condition that the next-to-leading term be also universal when F ̸= 0. and (ii) to explicitly derive the subleading term when (i) satisfies. This is physically important because we can obtain universal form of correlation function from this formula2. Furthermore, it is related to a log logL term of finite-size correction to grand-state energy density of a quantum spin chain, where L is a system size3. ∗This work is based on H. Mukaida J. Phys. A: Math Gen. 37 (2004) 10185, cond-mat/0405466. †[email protected] C. Itoi and H. Mukaida, Phys. Rev. E 60 (1999) 3688, cond-mat/9711308 D. J. Amit, Y. Y. Goldschmidt and G. G. Grinstein, J. Phys. A: Math. Gen. 13 (1980) 585 M-H. Kato, Renormalization Group Flows and Crossover Scaling Functions in Perturbed Coset Model, doctoral thesis (1998) Nihon University