3-states Potts model

introduction

• 3-states Potts model = M(5,6) minimal model
  
• two modular invariant partition functions
  
• c=4/5, effective central charge=4/5
  
• having the Z_3 symmetry W_3 algebra (W-algebra)
  

 

 

ferromagnetic three-state Potts spin chain

• [DKMM93]

 

 

 

 

conformal field theory

• discrete series unitary representations and GKO coset construction
  \(m= 5\)
  \(c = \frac{4}{5}\)
  \(h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}\)
  \(r = 1, 2, 3,4\) and \(s= 1, 2, 3,\cdots, r\) i.e. \(1\leq s\leq r< 5\)
  ( or \(1\leq r< s\leq m\) condition is also used)
  
• 10 irreducible representations
  
• conformal dimensions
  \(\Delta_{r,s}^{(p,p')}=h_{r,s}^{(p,p')}=\frac{(p'r-ps)^2-(p'-p)^2}{4pp'}\)
  \(1\leq r \leq p-1\) and \(1\leq s \leq p'-1\)
  note that \(\Delta_{r,s}^{(p,p')}=\Delta_{p-r,p'-s}^{(p,p')}\)
  r=1,2,3,4 s=1,2,3,4,5
  

 

 

 

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• parafermion theory
  

• table of minimal models
  
• rank 2 case
  
• W-algebra
  
• Schramm–Loewner evolution (SLE)
  
• Ising models
  
• hard hexagon model
  
• eight-vertex model and quantum XYZ model
  

 

 

encyclopedia

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

books

 

• 2010년 books and articles
  
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

4909919

 

 

articles

• Schramm–Loewner evolution in the three-state Potts model—a numerical study
  
  • Adam Gamsa and John Cardy J. Stat. Mech. (2007) P08020
• On thermodynamic approaches to conformal field theory
  
  • Jose Gaite, Nuclear Physics B Volume 525, Issue 3, 17 August 1998, Pages 627-640
    
• Critical exponents of the chiral Potts model from conformal field theory
  
  • John L. Cardy, 1993
    
• [DKMM93]Virasoro Characters from Bethe Equations for the Critical Ferromagnetic Three-State Potts Model
  
  • Srinandan Dasmahapatra, Rinat Kedem, Barry M. McCoy and Ezer Melzer, 1933
    
• Thermodynamics of the 3-state Potts Spin chain
  
  • Rinat Kedem, 1992
    
• Construction of Modular Branching Functions from Bethe’s Equations in the 3-State Potts Chain
  
  • Rinat Kedem, Barry M. McCoy, 1992
    
• Thermodynamic Bethe ansatz in relativistic models: Scaling 3-state potts and Lee-Yang models
  
  • Al. B. Zamolodchikov, 1990
    
• Integrals of Motion in Scaling 3-STATE Potts Model Field Theory.
  
  • Zamolodchikov, A, Volume: 3, Issue: 3(1988) pp. 743-750
    
• Conformal quantum field theory models in two dimensions having Z3 symmetry
  
  • V. A. Fateev and A. B. Zamolodchikov, Nuclear Phys. B 280 (1987), no. 4, 644–660
    
• Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models
  
  • Atsuo Kuniba, Yasuhiro Akutsu1 and Miki Wadati, 1986
• Critical behavior of the three-state Potts model: Monte Carlo renormalization group
  
  • Phys. Rev. B 28, 3897–3903 (1983)
    
• Critical exponents of the three-state potts model
  
  • Bambi Hu, 1980
    

• Hard hexagons: exact solution
  
  • R J Baxter 1980 J. Phys. A: Math. Gen.

• 논문정리
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html[1]
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
• http://dx.doi.org/10.1007/BF01049953
  

 

 

question and answers(Math Overflow)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences