Critical properties of the Blume-Emery-Griffiths model from the coherent-anomaly method

✍ Scribed by Gintautas Grigelionis; Saulius Lapinskas; Anders Rosengren

• Book ID: 104341343
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 376 KB
• Volume: 233
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/s0378-4371(96)00238-5

✦ Synopsis

We obtain the behaviour of the critical exponent ? in the Blume-Emery~riffiths model on the square and the triangular lattices crossing over from the spin-½ lsing critical regime to the Potts and to the ordinary tricritical regime. We use the coherent-anomaly method which scales the amplitudes of the leading divergencies obtained from the mean-field approximations. Even the minimal hierarchy of self-consistent approximations, provided by the cluster-variation method, yields very accurate estimates of 7 and critical temperatures, except close to the ordinary tricritical points, where the corrections to the classical value of ~ are very small. This also demonstrates the very good convergence of the cluster-variation approximations to the exact value.