Effective and asymptotic critical exponents of a weakly diluted quenched Ising model: Three-dimensional approach versus root epsilon expansion

Review

关键词: RENORMALIZATION-GROUP FUNCTIONS;    REPLICA-SYMMETRY-BREAKING;    ESTIMATING PERTURBATIVE COEFFICIENTS;    CRITICAL DISORDERED-SYSTEMS;    HIGH-MAGNETIC CONCENTRATION;    MONTE-CARLO SIMULATION;    SINGLE-ION-ANISOTROPY;    LARGE-ORDER BEHAVIOR;    QUANTUM-FIELD THEORY;    N-VECTOR MODEL;   

DOI  :  10.1103/PhysRevB.61.15114

来源: SCIE

【 摘 要 】

We present a field-theoretical treatment of the critical behavior of a three-dimensional weakly diluted quenched Ising model. To this end we analyze in the replica limit n-->0 the five-loop renormalization-group functions of the phi(4) theory with O(n)-symmetric and cubic interactions [H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995)]. The minimal subtraction scheme allows one to develop either the root epsilon-expansion series or to proceed within the three-dimensional approach, performing expansions in terms of renormalized couplings. Doing so, we compare both perturbation approaches and discuss their convergence and possible Borel summability. To study the crossover effect we calculate the effective critical exponents. We report resummed numerical values for the effective and asymptotic critical exponents. The results obtained within the three-dimensional approach agree pretty well with recent Monte Carlo simulations. root epsilon expansion does not allow reliable estimates for d=3.

【 授权许可】

Free