"3-states Potts model"의 두 판 사이의 차이
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| 25번째 줄: | 25번째 줄: | ||
* [[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> | * [[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> | ||
| − | |||
* 10 irreducible representations<br> | * 10 irreducible representations<br> | ||
| + | * 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> | ||
| 109번째 줄: | 109번째 줄: | ||
* [http://dx.doi.org/10.1016/0550-3213%2887%2990166-0 Conformal quantum field theory models in two dimensions having Z3 symmetry]<br> | * [http://dx.doi.org/10.1016/0550-3213%2887%2990166-0 Conformal quantum field theory models in two dimensions having Z3 symmetry]<br> | ||
** V. A. Fateev and A. B. Zamolodchikov, Nuclear Phys. B 280 (1987), no. 4, 644–660<br> | ** V. A. Fateev and A. B. Zamolodchikov, Nuclear Phys. B 280 (1987), no. 4, 644–660<br> | ||
| − | * | + | * [http://dx.doi.org/10.1143/JPSJ.55.3285 Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models]<br> |
** Atsuo Kuniba, Yasuhiro Akutsu1 and Miki Wadati, 1986 | ** Atsuo Kuniba, Yasuhiro Akutsu1 and Miki Wadati, 1986 | ||
* [http://dx.doi.org/10.1103/PhysRevB.28.3897 Critical behavior of the three-state Potts model: Monte Carlo renormalization group]<br> | * [http://dx.doi.org/10.1103/PhysRevB.28.3897 Critical behavior of the three-state Potts model: Monte Carlo renormalization group]<br> | ||
2010년 12월 4일 (토) 13:46 판
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
eight vertex model
history
- 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
- 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
- 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
- Srinandan Dasmahapatra, Rinat Kedem, Barry M. McCoy and Ezer Melzer, 1933
- Thermodynamics of the 3-state Potts Spin chain
- Rinat Kedem, 1992
- Rinat Kedem, 1992
- Construction of Modular Branching Functions from Bethe’s Equations in the 3-State Potts Chain
- Rinat Kedem, Barry M. McCoy, 1992
- Rinat Kedem, Barry M. McCoy, 1992
- Thermodynamic Bethe ansatz in relativistic models: Scaling 3-state potts and Lee-Yang models
- Al. B. Zamolodchikov, 1990
- 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
- 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
- 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)
- Phys. Rev. B 28, 3897–3903 (1983)
- Critical exponents of the three-state potts model
- Bambi Hu, 1980
- 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)
blogs
experts on the field