"3-states Potts model"의 두 판 사이의 차이

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==introduction==
 
==introduction==
  
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*  3-states Potts model = M(5,6) [[minimal models|minimal model]]<br>
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*  3-states Potts model = M(5,6) [[minimal models|minimal model]]
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*  two [[modular invariant partition functions]]<br>
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*  two [[modular invariant partition functions]]
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*  c=4/5, effective central charge=4/5<br>
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*  c=4/5, effective central charge=4/5
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*  having the Z_3 symmetry W_3 algebra ([[W-algebra]])<br>
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*  having the Z_3 symmetry W_3 algebra ([[W-algebra]])
  
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ferromagnetic three-state Potts spin chain
 
ferromagnetic three-state Potts spin chain
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* '''[DKMM93]'''
 
* '''[DKMM93]'''
  
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==conformal field theory==
 
==conformal field theory==
  
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* [[discrete series unitary representations|discrete series unitary representations and GKO coset construction]]<br><math>m= 5</math><br><math>c = \frac{4}{5}</math><br><math>h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}</math><br><math>r = 1, 2, 3,4</math> and <math>s= 1, 2, 3,\cdots, r</math> i.e. <math>1\leq s\leq r< 5</math><br> ( or <math>1\leq r< s\leq m</math> condition is also used)<br>
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* [[discrete series unitary representations|discrete series unitary representations and GKO coset construction]]
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*  10 irreducible representations<br>
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<math>m= 5, c = \frac{4}{5}</math>
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*  conformal dimensions<br><math>\Delta_{r,s}^{(p,p')}=h_{r,s}^{(p,p')}=\frac{(p'r-ps)^2-(p'-p)^2}{4pp'}</math><br><math>1\leq r \leq p-1</math> and <math>1\leq s \leq p'-1</math><br> note that <math>\Delta_{r,s}^{(p,p')}=\Delta_{p-r,p'-s}^{(p,p')}</math><br> r=1,2,3,4 s=1,2,3,4,5<br>
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:<math>h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}</math><math>r = 1, 2, 3,4</math> and <math>s= 1, 2, 3,\cdots, r</math> i.e. <math>1\leq s\leq r< 5</math> ( or <math>1\leq r< s\leq m</math> condition is also used)
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*  10 irreducible representations
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*  conformal dimensions
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:<math>\Delta_{r,s}^{(p,p')}=h_{r,s}^{(p,p')}=\frac{(p'r-ps)^2-(p'-p)^2}{4pp'}</math><math>1\leq r \leq p-1</math> and <math>1\leq s \leq p'-1</math>  
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* note that <math>\Delta_{r,s}^{(p,p')}=\Delta_{p-r,p'-s}^{(p,p')}</math> r=1,2,3,4 s=1,2,3,4,5
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==eight vertex model==
 
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==history==
 
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
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==related items==
 
==related items==
  
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* [[Z k parafermion theory|parafermion theory]]<br>
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* [[Z k parafermion theory|parafermion theory]]
  
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* [[table of minimal models]]<br>
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* [[table of minimal models]]
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* [[rank 2 case]]<br>
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* [[rank 2 case]]
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* [[W-algebra]]<br>
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* [[W-algebra]]
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* [[Schramm–Loewner evolution (SLE)]]<br>
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* [[Schramm–Loewner evolution (SLE)]]
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* [[Ising models]]<br>
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* [[Ising models]]
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* [[hard hexagon model]]<br>
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* [[hard hexagon model]]
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* [[eight-vertex model and quantum XYZ model]]<br>
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* [[eight-vertex model and quantum XYZ model]]
  
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==encyclopedia==
 
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* http://ko.wikipedia.org/wiki/
 
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* http://en.wikipedia.org/wiki/
 
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* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
 
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==books==
 
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* [[2010년 books and articles]]<br>
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
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[[4909919|4909919]]
 
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==articles==
 
==articles==
  
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* [http://dx.doi.org/10.1088/1742-5468/2007/08/P08020 Schramm–Loewner evolution in the three-state Potts model—a numerical study]<br>
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* [http://dx.doi.org/10.1088/1742-5468/2007/08/P08020 Schramm–Loewner evolution in the three-state Potts model—a numerical study]
 
** Adam Gamsa and John Cardy J. Stat. Mech. (2007) P08020
 
** Adam Gamsa and John Cardy J. Stat. Mech. (2007) P08020
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* [http://dx.doi.org/10.1016/S0550-3213%2898%2900340-X On thermodynamic approaches to conformal field theory]<br>
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* [http://dx.doi.org/10.1016/S0550-3213%2898%2900340-X On thermodynamic approaches to conformal field theory]
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**  Jose Gaite, Nuclear Physics B Volume 525, Issue 3, 17 August 1998, Pages 627-640<br>
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**  Jose Gaite, Nuclear Physics B Volume 525, Issue 3, 17 August 1998, Pages 627-640
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* [http://dx.doi.org/10.1016/0550-3213%2893%2990353-Q Critical exponents of the chiral Potts model from conformal field theory]<br>
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* [http://dx.doi.org/10.1016/0550-3213%2893%2990353-Q Critical exponents of the chiral Potts model from conformal field theory]
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**  John L. Cardy, 1993<br>
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**  John L. Cardy, 1993
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* '''[DKMM93]'''[http://dx.doi.org/10.1007/BF02186814 Virasoro Characters from Bethe Equations for the Critical Ferromagnetic Three-State Potts Model]<br>
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* '''[DKMM93]'''[http://dx.doi.org/10.1007/BF02186814 Virasoro Characters from Bethe Equations for the Critical Ferromagnetic Three-State Potts Model]
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**  Srinandan Dasmahapatra, Rinat Kedem, Barry M. McCoy and Ezer Melzer, 1933<br>
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**  Srinandan Dasmahapatra, Rinat Kedem, Barry M. McCoy and Ezer Melzer, 1933
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* [http://dx.doi.org/10.1007/BF01049954 Thermodynamics of the 3-state Potts Spin chain]<br>
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* [http://dx.doi.org/10.1007/BF01049954 Thermodynamics of the 3-state Potts Spin chain]
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**  Rinat Kedem, 1992<br>
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**  Rinat Kedem, 1992
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* [http://dx.doi.org/10.1007/BF01049953 Construction of Modular Branching Functions from Bethe’s Equations in the 3-State Potts Chain]<br>
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* [http://dx.doi.org/10.1007/BF01049953 Construction of Modular Branching Functions from Bethe’s Equations in the 3-State Potts Chain]
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**  Rinat Kedem, Barry M. McCoy, 1992<br>
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**  Rinat Kedem, Barry M. McCoy, 1992
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* [http://dx.doi.org/10.1016/0550-3213%2890%2990333-9 Thermodynamic Bethe ansatz in relativistic models: Scaling 3-state potts and Lee-Yang models]<br>
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* [http://dx.doi.org/10.1016/0550-3213%2890%2990333-9 Thermodynamic Bethe ansatz in relativistic models: Scaling 3-state potts and Lee-Yang models]
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**  Al. B. Zamolodchikov, 1990<br>
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**  Al. B. Zamolodchikov, 1990
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* [http://dx.doi.org/10.1142/S0217751X88000333 Integrals of Motion in Scaling 3-STATE Potts Model Field Theory].<br>
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* [http://dx.doi.org/10.1142/S0217751X88000333 Integrals of Motion in Scaling 3-STATE Potts Model Field Theory].
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**  Zamolodchikov, A, Volume: 3, Issue: 3(1988) pp. 743-750<br>
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**  Zamolodchikov, A, Volume: 3, Issue: 3(1988) pp. 743-750
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* [http://dx.doi.org/10.1016/0550-3213%2887%2990166-0 Conformal quantum field theory models in two dimensions having Z3 symmetry]<br>
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* [http://dx.doi.org/10.1016/0550-3213%2887%2990166-0 Conformal quantum field theory models in two dimensions having Z3 symmetry]
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**  V. A. Fateev and A. B. Zamolodchikov, Nuclear Phys. B 280 (1987), no. 4, 644–660<br>
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**  V. A. Fateev and A. B. Zamolodchikov, Nuclear Phys. B 280 (1987), no. 4, 644–660
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* [http://dx.doi.org/10.1143/JPSJ.55.3285 Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models]<br>
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* [http://dx.doi.org/10.1143/JPSJ.55.3285 Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models]
 
** Atsuo Kuniba, Yasuhiro Akutsu1 and Miki Wadati, 1986
 
** Atsuo Kuniba, Yasuhiro Akutsu1 and Miki Wadati, 1986
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* [http://dx.doi.org/10.1103/PhysRevB.28.3897 Critical behavior of the three-state Potts model: Monte Carlo renormalization group]<br>
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* [http://dx.doi.org/10.1103/PhysRevB.28.3897 Critical behavior of the three-state Potts model: Monte Carlo renormalization group]
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**  Phys. Rev. B 28, 3897–3903 (1983)<br>
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**  Phys. Rev. B 28, 3897–3903 (1983)
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* [http://dx.doi.org/10.1016/0375-9601%2880%2990300-X Critical exponents of the three-state potts model]<br>
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* [http://dx.doi.org/10.1016/0375-9601%2880%2990300-X Critical exponents of the three-state potts model]
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**  Bambi Hu, 1980<br>
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**  Bambi Hu, 1980
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* [http://dx.doi.org/10.1088/0305-4470/13/3/007 Hard hexagons: exact solution]
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* [http://dx.doi.org/10.1088/0305-4470/13/3/007 Hard hexagons: exact solution]<br>
 
 
** R J Baxter 1980 J. Phys. A: Math. Gen.
 
** R J Baxter 1980 J. Phys. A: Math. Gen.
  
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* [[2010년 books and articles|논문정리]]
 
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* http://pythagoras0.springnote.com/
 
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html][http://www.ams.org/mathscinet ]
 
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* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
 
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* 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=
 
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* http://dx.doi.org/10.1007/BF01049953<br>
 
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==question and answers(Math Overflow)==
 
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* http://mathoverflow.net/search?q=
 
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* http://mathoverflow.net/search?q=
 
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==blogs==
 
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==experts on the field==
 
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* http://arxiv.org/
 
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==links==
 
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* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]
 
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* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
 
 
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q7235385 Q7235385]
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===Spacy 패턴 목록===
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* [{'LOWER': 'potts'}, {'LEMMA': 'model'}]

2021년 2월 17일 (수) 02:51 기준 최신판

introduction



ferromagnetic three-state Potts spin chain

  • [DKMM93]



conformal field theory

\(m= 5, c = \frac{4}{5}\) \[h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}\]\(r = 1, 2, 3,4\) 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



related items



articles

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'potts'}, {'LEMMA': 'model'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=3-states_Potts_model&oldid=51847"