Critical exponents of the three-dimensional Blume–Capel model on a cellular automaton

✍ Scribed by A. Özkan; N. Seferoğlu; B. Kutlu

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 294 KB
• Volume: 362
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2005.08.065

✦ Synopsis

The static critical exponents of the three-dimensional Blume-Capel model which has a tricritical point at D=J ¼ 2:82 value are estimated for the standard and the cooling algorithms which improved from Creutz cellular automaton. The analyses of the data using the finite-size scaling and power-law relations reproduce their well-established values in the D=Jo3 and D=Jo2:8 parameter region at standard and cooling algorithms, respectively. For the cooling algorithm at D=J ¼ 2:8 value of single-ion anisotropy parameter, the static critical exponents are estimated as b ¼ 0:31, g ¼ g 0 ¼ 1:6, a ¼ a 0 ¼ 0:32 and n ¼ 0:87. These values are different from b ¼ 0:31, g ¼ g 0 ¼ 1:25, a ¼ a 0 ¼ 0:12 and n ¼ 0:64 universal values. This case indicated that the BC model exhibits an ununiversal critical behavior at the D=J ¼ 2:8 parameter value near the tricritical point (D=J ¼ 2:82). The simulations were carried out on a simple cubic lattice with periodic boundary conditions.