Hamiltonian studies of phase diagrams of lattice gauge theories and spin systems

Thesis/Dissertation · Tue Jan 01 00:00:00 EST 1980

OSTI ID:5192391

Banks, J L

Hamiltonian lattice methods are used to study gauge theories with discrete symmetries coupled to scalar fields, and magnetic systems with continuous symmetries. After the general method is introduced, and applied to the Z/sub 2/ pure gauge theory as an example, it is employed in an analysis of the phase diagram of the same theory coupled to Higgs fields, in 2 + 1 dimensions. Strong coupling expansions and Pade approximants are used to find zeros of the mass gap in the latter theory, which indicate second-order phase transitions. The results are qualitatively in agreement with what is expected from arguments based on the partition-function formulation of the theory. First-order transitions, which have been found by other methods, are also discussed for similar theories, in the context of a (1/N) expansion. The Hamiltonian formulation is also used to study the lattice version of the Callan-Symanzik ..beta..-function, for the mean spherical model in 1 + 1 dimensions. A strong coupling expansion is obtained for this function, and extrapolated using one- and two-point Pade approximants. The latter are matched onto the perturbative weak-coupling expression for the ..beta..-function of the continuum O(n) sigma-model, in the large n limit. The results are a reasonably smooth connection between strong and weak coupling, and quite good agreement with the exact solution. Both of these aspects of the result lend encouragement to the ongoing attempts to study four-dimensional non-Abelian gauge theories, and in particular the question of quark confinement, using the Hamiltonian strong-coupling approach.

• Research Organization: Cornell Univ., Ithaca, NY (USA)
• OSTI ID: 5192391
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
LATTICE FIELD THEORY
HAMILTONIANS
PHASE DIAGRAMS
SIGMA MODEL
SPHERICAL MODEL
STRONG-COUPLING MODEL
SYMMETRY
WEAK-COUPLING MODEL
DIAGRAMS
FIELD THEORIES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
NUCLEAR MODELS
PARTICLE MODELS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
645400* - High Energy Physics- Field Theory