Study of. lambda. parameters and crossover phenomena in SU(N) x SU(N) sigma models in two dimensions

Technical Report · Thu Jan 01 00:00:00 EST 1981

DOI:https://doi.org/10.2172/6522949· OSTI ID:6522949

Shigemitsu, J; Kogut, J B

The spin system analogues of recent studies of the string tension and ..lambda.. parameters of SU(N) gauge theories in 4 dimensions are carried out for the SU(N) x SU(N) and O(N) models in 2 dimensions. The relations between the ..lambda.. parameters of both the Euclidean and Hamiltonian formulation of the lattice models and the ..lambda.. parameter of the continuum models are obtained. The one loop finite renormalization of the speed of light in the lattice Hamiltonian formulations of the O(N) and SU(N) x SU(N) models is calculated. Strong coupling calculations of the mass gaps of these spin models are done for all N and the constants of proportionality between the gap and the ..lambda.. parameter of the continuum models are obtained. These results are contrasted with similar calculations for the SU(N) gauge models in 3+1 dimensions. Identifying suitable coupling constants for discussing the N ..-->.. infinity limits, the numerical results suggest that the crossover from weak to strong coupling in the lattice O(N) models becomes less abrupt as N increases while the crossover for the SU(N) x SU(N) models becomes more abrupt. The crossover in SU(N) gauge theories also becomes more abrupt with increasing N, however, at an even greater rate than in the SU(N) x SU(N) spin models.

• Research Organization: Brown Univ., Providence, RI (USA). Dept. of Physics; Illinois Univ., Urbana (USA). Dept. of Physics
• Sponsoring Organization: USDOE
• DOE Contract Number: AC02-76ER03130
• OSTI ID: 6522949
• Report Number(s): DOE/ER/03130-T2; TRN: 81-007927
• Country of Publication: United States
• Language: English

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645400* - High Energy Physics- Field Theory