On the estimation of the equilibrium properties of the kinetic Ising model of ferromagnetism

✍ Scribed by C.H.J. Johnson

• Book ID: 103048126
• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 769 KB
• Volume: 14
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(78)90014-0

✦ Synopsis

Using a comparatively small group of spin ~paiticles set on a simple cubic lattice, an attempt has been made to obtain satisfactory simulation estimates of the equilibrium critical properties of the three-dimensional Ising system. Assuming only nearest-neighbout interactions and regarding a 10 X 10 X 10 particle group as a sample from the infinite system, the states of the nearest-neighbour external particles were estimated in a self-consistent manner using probability distribution functions whose moments are equal to the sample moments (particle correlation functions). We obtained in this way a value of 4.45 ±0.05 (in units of f/kB) for the critical temperature for the long-range order with exponent 0.31 ±0.04. These values campare favourably with the expected theoretical values obtained from series expansions. The results for specific heat are less satisfactory. Analytical results have been obtained for the two-particle sample and we find a critical temperature of 4.46, but with a critical exponent of 1.05 for the long-range order.