Loading...

Solvability of 2-D Models of Statistical Mechanics and its Relation to Discretely Holomorphic Parafermions at Critical Points

Tanhayi Ahari, Mostafa | 2011

400 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42846 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rouhani, Shahin
  7. Abstract:
  8. Discretely holomorphic observables have recently been proposed for two dimensional lattice models at criticality, whose correlation functions satisfy a discrete version of Cauchy-Riemann relations. Existence of these observables appears to have a deep relation with integrability of the model. On the other hand at critical points of these models, there exist entities known as discrete parafermions whose Boltzmann weights satisfy the Yang-Baxter Equations. For this reason, finding parafermionic observables in any lattice model is equivalent to proof of solvability. This thesis is a step towards understanding the relation between Parafermions and Solvability. For instance, the Boltzmann weights of solvable O(n) model are the same Boltzmann weights obtained for the discretely holomorphic parafermions. These observables are presumably the lattice versions of the holomorphic observables appearing in the conformal field theory (CFT). In this thesis, we offer a review of the concept of solvability, and then we proceed with introducing holomorphic parafermions. We note that these observables are only defined at critical points and solvable region of the models. This project could be an initial step towards understanding the relations between integrablity, CFT and the scaling limits of the statistical mechanical models at critical points.

  9. Keywords:
  10. Conformal Fields Theory ; O(N) Model ; Discretely Holomorphic Observables ; Yang-Baxter Equations

 Digital Object List

 Bookmark

No TOC