The Ashkin-Teller and q-state Potts models, on the square and triangular lattices, are studied by approximate methods. A series analysis is used to investigate the variation, with q, of the internal energy and specific heat of the Potts model. Estimates of the specific heat exponents are given. A number of real-space renormalization groups are then used to study both models. The decimation and cluster expansion values, for the critical temperature and exponents, imply that larger clusters are needed in order to obtain reliable quantitative results, although even the simplest of these transformations gave an accurate qualitative description of the critical surface of the Ashkin-Teller model. The lower bound variational renormalization group is modified to allow an investigation of the two-layer using representation of the square lattice Ashkin-Teller model. Wherever exact results are available, the transformation proves to be remarkably accurate. A line of fixed points is found, giving exponents which vary continuously with interaction strength. A comparison with the corresponding results for the eight vertex model indicates that, for the same ratio, of four to two-spin couplings, the models have equal exponents.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:635801 |
| Date | January 1979 |
| Creators | Ashley, S. E. |
| Publisher | Swansea University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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