Real-space renormalization-group scheme for spin and gauge systems

Journal Article · Thu Nov 15 04:00:00 EST 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.20.2566· OSTI ID:5727536

Fradkin, E; Raby, S

We present a real-space renormalization-group scheme for both spin and gauge systems within a Hamiltonian formalism. The approximation, in particular, preserves gauge invariance at every step of the calculation. We apply this scheme to the (1+1) -dimensional Ising model in a transverse field and to the (2+1) -dimensional Ising gauge theory. We find reasonable results for the critical coupling and for those critical exponents which are related to energy gaps. We also obtain the correct qualitative behavior for order and disorder parameters and correlation functions. In particular, the calculation yields exponential decay for correlation functions in the disordered phase. However, the critical indices we find for spacelike quantities are not good. This defect of the approximation is related to the asymmetric scaling of space and time under the renormalization group.

• Research Organization: Department of Physics, Institute of Theoretical Physics, Stanford University, Stanford, California 94305
• OSTI ID: 5727536
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 20:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BOUNDARY CONDITIONS
CORRELATION FUNCTIONS
COUPLING CONSTANTS
CRYSTAL MODELS
FUNCTIONS
GAUGE INVARIANCE
HAMILTONIANS
INVARIANCE PRINCIPLES
ISING MODEL
LATTICE FIELD THEORY
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
PARTICLE PROPERTIES
QUANTUM MECHANICS
QUANTUM OPERATORS
RENORMALIZATION
SCALING LAWS
SPACE-TIME
SPIN