| Autor: |
See Kit Foong, Jorge L. Delyra, Arie Kapulkin, Rob Harrington, T. E. Gallivan, Eric Myers, Bryce S. DeWitt, Joseph Polchinski |
| Rok vydání: |
1992 |
| Předmět: |
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| Zdroj: |
Physical Review D. 46:2538-2552 |
| ISSN: |
0556-2821 |
| DOI: |
10.1103/physrevd.46.2538 |
| Popis: |
A lattice formulation of the $\frac{\mathrm{O}(1,2)}{\mathrm{O}(2)\ifmmode\times\else\texttimes\fi{}{Z}_{2}}$ sigma model is developed, based on the continuum theory presented in the preceding paper. Special attention is given to choosing a lattice action (the "geodesic" action) that is appropriate for fields having noncompact curved configuration spaces. A consistent continuum limit of the model exists only if the renormalized scale constant ${\ensuremath{\beta}}_{R}$ vanishes for some value of the bare scale constant $\ensuremath{\beta}$. The geodesic action has a special form that allows direct access to the small-$\ensuremath{\beta}$ limit. In this limit half of the degrees of freedom can be integrated out exactly. The remaining degrees of freedom are those of a compact model having a $\ensuremath{\beta}$-independent action which is noteworthy in being unbounded from below yet yielding integrable averages. Both the exact action and the $\ensuremath{\beta}$-independent action are used to obtain ${\ensuremath{\beta}}_{R}$ from Monte Carlo computations of field-field averages (two-point functions) and current-current averages. Many consistency cross-checks are performed. It is found that there is no value of $\ensuremath{\beta}$ for which ${\ensuremath{\beta}}_{R}$ vanishes. This means that as the lattice cutoff is removed the theory becomes that of a pair of massless free fields. Because these fields have neither the geometry nor the symmetries of the original model we conclude that the $\frac{\mathrm{O}(1,2)}{\mathrm{O}(2)\ifmmode\times\else\texttimes\fi{}{Z}_{2}}$ model has no continuum limit. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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