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| In [[theoretical physics]], the '''minimal models''' are a very concrete well-defined type of [[rational conformal field theory]]. The individual minimal models are parameterized by two integers ''p,q'' that are moreover related for the unitary minimal models.
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| ==Classification==
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| * <math> c = 1 - 6 {(p-q)^2 \over pq}</math>
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| * <math> h = h_{r,s}(c) = {{(pr-qs)^2-(p-q)^2} \over 4pq}</math>
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| These conformal field theories have a finite set of conformal families which close under fusion. However, generally these will not be unitary. Unitarity imposes the further restriction that q and p are related by q=m and p=m+1.
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| :<math> c = 1-{6\over m(m+1)} = 0,\quad 1/2,\quad 7/10,\quad 4/5,\quad 6/7,\quad 25/28, \ldots</math>
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| for ''m'' = 2, 3, 4, .... and ''h'' is one of the values
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| :<math> h = h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}</math>
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| for ''r'' = 1, 2, 3, ..., ''m''−1 and ''s''= 1, 2, 3, ..., ''r''.
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| The first few minimal models correspond to central charges and dimensions:
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| *''m'' = 3: ''c'' = 1/2, ''h'' = 0, 1/16, 1/2. These 3 representations are related to the [[Ising model]] at criticality. The three operators correspond to the identity, spin and energy density respectively.
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| *''m'' = 4: ''c'' = 7/10. ''h'' = 0, 3/80, 1/10, 7/16, 3/5, 3/2. These 6 give the scaling fields of the tri critical [[Ising model]].
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| *''m'' = 5: ''c'' = 4/5. These give the 10 fields of the 3-state [[Potts model]].
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| *''m'' = 6: ''c'' = 6/7. These give the 15 fields of the tri critical 3-state [[Potts model]].
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| ==References==
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| * P. Di Francesco, P. Mathieu, and D. Sénéchal, ''Conformal Field Theory'', [[Springer Science+Business Media|Springer-Verlag]], [[New York]], 1997. ISBN 0-387-94785-X.
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| {{DEFAULTSORT:Minimal Models}}
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| [[Category:Conformal field theory]]
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| [[Category:Exactly solvable models]]
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| {{Phys-stub}}
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