Lattice renormalization of phi/sup 4/ theory
Thesis/Dissertation
·
OSTI ID:6082271
The present work employs a non-perturbative numerical method to study the phi/sup 4/ theory in four dimensions. The Euclidean momentum space two- and four-point functions are computed using path integrals after lattice- and finite-volume-cutoffs have reduced these integrals from infinite to N dimensions. These integrals are regarded as moments of a probability measure on field configuration space and evaluated on a computer using Monte Carlo techniques. The probability distribution for the field phi(chi) at each lattice site chi, given by the exponential of the lattice phi/sup 4/ action, is factored into a part depending only on phi(chi) and a part depending on phi(chi) and its nearest neighbor field variables; the heat bath algorithm is used to generate the first factor and the Metropolis method the second. From the two-point function a lattice version of the correlation length (related to the Compton wavelength of the lightest state) is computed. From the four- and two-point functions the renormalized coupling constant lambda/sub R/ is computed. Renormalization is carried out by varying the bare coupling constant lambda/sub 0/ and lattice size N while keeping fixed the physical length L of the lattice and the correlation length. (Keeping the correlation length fixed requires adjustment of the bare mass.) Computations were performed wth N = 3/sup 4/, 4/sup 4/, 6/sup 4/, 10/sup 4/. The resulting plots of lambda/sub R/ vs. lambda/sub 0/ monotonically and uniformly tend to zero as N increases. There is no evidence that in the continuum limit (N ..-->.. Infinity) lambda/sub R/ can be made nonzero and the theory interacting. As lambda/sub 0/ ..-->.. Infinity the theory approaches the spin-1/2 Ising model. Independent numerical computations on this system agree with the results for large lambda/sub 0/.
- Research Organization:
- Indiana Univ., Bloomington (USA)
- OSTI ID:
- 6082271
- Country of Publication:
- United States
- Language:
- English
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