Accurate Monte Carlo critical exponents for Ising lattices

✍ Scribed by Jorge Garcı́a; Julio A Gonzalo

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 209 KB
• Volume: 326
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/s0378-4371(03)00362-5

✦ Synopsis

A careful Monte Carlo investigation of the phase transition very close to the critical point (T → Tc, H → 0) in relatively large d = 3, s = 1 2 Ising lattices did produce critical exponents ÿ3D = 0:3126(4) ∼ = 5=16, -1 3D = 0:1997(4) ∼ = 1=5 and 3D = 1:253(4) ∼ = 5=4. Our results indicate that, within experimental error, they are given by simple fractions corresponding to the linear interpolations between the respective two dimensional (Onsager) and four dimensional (mean ÿeld) critical exponents. An analysis of our inverse susceptibility data -1 (T ) vs. |T -Tc| shows that these data lead to a value of 3D compatible with = and Tc = 4:51152(12), while values obtained recently by high and low temperature series expansions and renormalization group methods are not.