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Ising critical exponents
This article lists the critical exponents of the ferromagnetic transition in the Ising model. In statistical physics, the Ising model describes a continuous phase transition with scalar order parameter. The critical exponents of the transition are universal values and characterise the singular properties of physical quantities. The ferromagnetic transition of the Ising model establishes an important universality class, which contains a variety of phase transitions as different as ferromagnetism close to the Curie point and critical opalescence of liquid near its critical point.
| d | 2 | 3 | 4 |
|---|---|---|---|
| α | 0 | 0.110(1) | 0 |
| β | 1/8 | 0.3265(3) | 1/2 |
| γ | 7/4 | 1.2372(5) | 1 |
| δ | 15 | 4.789(2) | 3 |
| η | 1/4 | 0.0364(5) | |
| ν | 1 | 0.6301(4) | 1/2 |
| ω | 2 | 0.84(4) |
The values for d=3 are the most recent and precise estimates taken from Ref.[1] and Ref.[2] References to the original works may be found therein. The values for d=2 are exact and may also be found in Ref.[1] The values for d=4 are exact and correspond to the results of mean-field theory, e.g., Ginzburg-Landau theory (reference missing).
More information on critical exponents may be found at SklogWiki
References
Pelissetto, Andrea; Vicari, Ettore (2002). "Critical phenomena and renormalization-group theory". Physics Reports 368 (6): 549–727. arXiv:cond-mat/0012164. Bibcode:2002PhR...368..549P. doi:10.1016/S0370-1573(02)00219-3.
Kleinert, H., "Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions". Physical Review D 60, 085001 (1999)
Books
Kleinert, H. and Schulte-Frohlinde, V.; Critical Properties of φ4-Theories, World Scientific (Singapore, 2001); Paperback ISBN 981-02-4658-7 (also available online) (together with V. Schulte-Frohlinde)
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