Renormalization Group Calculations for (1) Symmetric Spin Systems and Gauge Theories
Mar, 198041 pages
Published in:
- Phys.Rev.D 24 (1981) 941
Report number:
- Print-80-0213 (UC,SANTA BARBARA)
Citations per year
Abstract: (APS)
We present a real-space renormalization-group analysis for the U(1) spin model in two and three dimensions and for compact electrodynamics in three and four dimensions. The Hamiltonian formulation of the theory defined on a hypercubic spatial lattice is used. The nonperturbative renormalization-group transformations we derive give continuous phase transitions for the spin models, in two and three dimensions. In three dimensions the gap exponent agrees remarkably well with series-expansion results. For the gauge theory we find, in agreement with Polyakov, that compact electrodynamics in three dimensions confines for all values of the coupling constant. A calculation for the string tension shows that it vanishes with an essential singularity at zero coupling. In four dimensions for weak enough coupling confinement is lost and the theory shows a phase transition between a charge-confining and a freephoton phase.- GAUGE FIELD THEORY: U(1)
- LATTICE FIELD THEORY
- MODEL: SPIN
- SPIN: MODEL
- GAUGE FIELD THEORY: TWO-DIMENSIONAL
- GAUGE FIELD THEORY: THREE-DIMENSIONAL
- GAUGE FIELD THEORY: FOUR-DIMENSIONAL
- GAUGE FIELD THEORY: NONPERTURBATIVE
- RENORMALIZATION GROUP: TRANSFORMATION
- GAUGE FIELD THEORY: CRITICAL PHENOMENA
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