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Finite Size Effect in SLE(k,p)

Amir Bagheri, Amir Ali | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40482 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Moghimi Araghi, Saman
  7. Abstract:
  8. Conformal Field Theory provides an efficient method for studying physical problems in critical point. Correlation length becomes converge in this point. It can also be clarified that some curves are observed in geometrical phase transition which are conformal invariant and they can be studied using SLE(k). The first mathematical generalization of SLE(k) while keeping the self-similarity property, leads to SLE(k,p). Conformal field theory and SLE are interrelated and their parameters are interpretable for each other. One usually studies the problem in the upper-half plane. Here we consider the problem using a map like (w=L/π Ln z) between the upper-half plane and a special region (e.g. a strip with its width equal to L). During this research we focus on the Fermionic action and its solution on the previously mentioned strip. It should be added that in the action we work with Grassmanian fields. Finally, the Helmholtz free energy per unit length of the strip is obtained upon the Grasmanian algebra generators and the modifications on the central charge have been implemented.
  9. Keywords:
  10. Conformal Fields Theory ; Schramm-Loewner Evolution (SLE) ; Geometrical Phase Transform ; Finite Size Effect ; Grassmanien Algebra

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  • فصل اول:
  • پدیده های تصادفی
    • (1-1)مقدمه:
  • فصل دوم:
  • مقدمه اي بر نظريه ميدان همديس
  • (2-1) مقدمه:
    • (2-2) نگاشت همديس در حالت كلي :
    • (2-3) تانسور انرژي تكانه و بار مركزي :
    • (2-4 ) كوانتش شعاعي و جبر ويراسورو:
  • آشنايي با SLE
    • (3-1) مقدمه:
    • (3-2) مدل آيزينگ و منحني هاي تصادفي :
      • ((1-2-3 فرايند كاوش:
    • SLE(3-3)
      • (1-3-3) اصول موضوعهSLE:
      • (3-3-2 ) معادله لونر:
      • (3-3-3) تحول شرم- لونر:
      • (4-2-3) برخي از خواص SLE:
    • (3-3) محاسبه توسط SLE:
      • (1-3-3) فرمول "شرم":
      • (3-3-2 ) محاسبه برخي از نماهاي بحراني توسط SLE:
    • (4-3) ارتباط SLE و نظريه ميدان همديس18F :
      • (1-4-3 ) خم ها و حالت ها:
  • فصل چهارم
  • SLE(κ ,ρ) و مدل گاز كولني و اثر طول محدود
    • (4-1) مقدمه:
    • /// /(2-4 ) نظريه ميدان همديس و منحني هاي SLE(κ ,ρ):
    • (4-3) نظريه ميدان آزاد:
    • (4-4) اثرطول محدود20F :
  • فصل پنجم:
  • اثر طول محدود در کنش فرمیونی
    • (1-5) مقدمه:
    • (2-5) میدان فرمیونی آزاد و عملگرهای شرط مرزی عوض کن فرمیونی:
    • (3-5) اثر طول محدود و محاسبه‏ی انرژی آزاد هلمهولتز بر واحد طول نوارکنش فرميوني:
  • فهرست منابع و ماخذ:
  • [1] J.Cardy, “Conformal Invariance in Percolation, Self-Avoiding Walks and Related Problems” (arXiv:cond-mat/0209638v2)
  • [20] S. Moghimi-Araghi, M. A. Rajabpour, S. Rouhani “SLE(κ,ρ)and Boundary Coulomb Gas” (arXiv:hep-th/0508047v1)
  • Abstract
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