Real-space dynamic renormalization group. III. Calculation of correlation functions

Journal Article · Sun Feb 01 04:00:00 EST 1981 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.23.1431· OSTI ID:6654565

Mazenko, G F; Hirsch, J E; Nolan, M J; Valls, O T

The real-space dynamic renormalization group method developed in previous papers is applied to the kinetic Ising model defined on a square lattice. In particular we extend the formalism to the calculation of space- and time-dependent equilibrium averaged correlation functions. We find that conventional methods for implementing the real-space renormalization group via cumulant expansions in terms of the intercell coupling lead to correlation functions which decay algebraically in space at large distances in the disordered phase in qualitative disagreement with the known exponential decay. We indicate how one can develop new perturbation theory expansion methods which lead to the proper exponential decay at large distances and also lead to good quantitative results for other observable quantities like the magnetization, susceptibility, and single spin time autocorrelation function. As the result of a first-order calculation we obtain excellent results for the static critical exponents and a value of z=1.79 for the dynamic critical exponent. The critical exponents obtained from the correlation functions calculated using this method satisfy the proper static and dynamic scaling relations.

• Research Organization: The James Franck Institute and the Department of Physics, University of Chicago, Chicago, Illinois 60637
• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 6654565
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Journal Name: Phys. Rev. B: Condens. Matter; (United States) Vol. 23:3; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

656000* -- Condensed Matter Physics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CORRELATION FUNCTIONS
CRYSTAL MODELS
FUNCTIONS
ISING MODEL
MAGNETIC PROPERTIES
MAGNETIC SUSCEPTIBILITY
MAGNETIZATION
MATHEMATICAL MODELS
PERTURBATION THEORY
PHYSICAL PROPERTIES
RENORMALIZATION
SCALING LAWS