"3-states Potts model"의 두 판 사이의 차이
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| − | + | ==introduction== | |
| − | * 3-states Potts model = | + | * 3-states Potts model = M(5,6) [[minimal models|minimal model]] |
| − | * | + | * two [[modular invariant partition functions]] |
| − | * c=4/5, effective central charge=4/5 | + | * c=4/5, effective central charge=4/5 |
| − | * having the | + | * having the Z_3 symmetry W_3 algebra ([[W-algebra]]) |
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| − | + | ferromagnetic three-state Potts spin chain | |
| − | * | + | * '''[DKMM93]''' |
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| − | + | ==conformal field theory== | |
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| − | + | * [[discrete series unitary representations|discrete series unitary representations and GKO coset construction]] | |
| + | <math>m= 5, c = \frac{4}{5}</math> | ||
| + | :<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) | ||
| + | * 10 irreducible representations | ||
| + | * conformal dimensions | ||
| + | :<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> | ||
| + | * 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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| − | + | ==related items== | |
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| − | + | * [[Z k parafermion theory|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]] | ||
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| − | + | ==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] |
| + | ** Adam Gamsa and John Cardy J. Stat. Mech. (2007) P08020 | ||
| + | * [http://dx.doi.org/10.1016/S0550-3213%2898%2900340-X On thermodynamic approaches to conformal field theory] | ||
| + | ** Jose Gaite, Nuclear Physics B Volume 525, Issue 3, 17 August 1998, Pages 627-640 | ||
| + | * [http://dx.doi.org/10.1016/0550-3213%2893%2990353-Q Critical exponents of the chiral Potts model from conformal field theory] | ||
| + | ** John L. Cardy, 1993 | ||
| + | * '''[DKMM93]'''[http://dx.doi.org/10.1007/BF02186814 Virasoro Characters from Bethe Equations for the Critical Ferromagnetic Three-State Potts Model] | ||
| + | ** Srinandan Dasmahapatra, Rinat Kedem, Barry M. McCoy and Ezer Melzer, 1933 | ||
| + | * [http://dx.doi.org/10.1007/BF01049954 Thermodynamics of the 3-state Potts Spin chain] | ||
| + | ** Rinat Kedem, 1992 | ||
| + | * [http://dx.doi.org/10.1007/BF01049953 Construction of Modular Branching Functions from Bethe’s Equations in the 3-State Potts Chain] | ||
| + | ** Rinat Kedem, Barry M. McCoy, 1992 | ||
| + | * [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] | ||
| + | ** Al. B. Zamolodchikov, 1990 | ||
| + | * [http://dx.doi.org/10.1142/S0217751X88000333 Integrals of Motion in Scaling 3-STATE Potts Model Field Theory]. | ||
| + | ** Zamolodchikov, A, Volume: 3, Issue: 3(1988) pp. 743-750 | ||
| + | * [http://dx.doi.org/10.1016/0550-3213%2887%2990166-0 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 | ||
| + | * [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 | ||
| + | * [http://dx.doi.org/10.1103/PhysRevB.28.3897 Critical behavior of the three-state Potts model: Monte Carlo renormalization group] | ||
| + | ** Phys. Rev. B 28, 3897–3903 (1983) | ||
| + | * [http://dx.doi.org/10.1016/0375-9601%2880%2990300-X Critical exponents of the three-state potts model] | ||
| + | ** Bambi Hu, 1980 | ||
| + | * [http://dx.doi.org/10.1088/0305-4470/13/3/007 Hard hexagons: exact solution] | ||
| + | ** R J Baxter 1980 J. Phys. A: Math. Gen. | ||
| − | + | [[분류:integrable systems]] | |
| + | [[분류:math and physics]] | ||
| + | [[분류:migrate]] | ||
| − | + | ==메타데이터== | |
| − | + | ===위키데이터=== | |
| − | + | * ID : [https://www.wikidata.org/wiki/Q7235385 Q7235385] | |
| − | + | ===Spacy 패턴 목록=== | |
| − | + | * [{'LOWER': 'potts'}, {'LEMMA': 'model'}] | |
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2021년 2월 17일 (수) 01:51 기준 최신판
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
\(m= 5, c = \frac{4}{5}\) \[h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}\]\(r = 1, 2, 3,4\) 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
- 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
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.
메타데이터
위키데이터
- ID : Q7235385
Spacy 패턴 목록
- [{'LOWER': 'potts'}, {'LEMMA': 'model'}]