Some results on hyperscaling in the 3D Ising model
- Los Alamos National Lab., NM (United States). Theoretical Div.
- Univ. of Tokyo (Japan). Dept. of Physics
The authors review exact studies on finite-sized 2 dimensional Ising models and show that the point for an infinite-sized model at the critical temperature is a point of nonuniform approach in the temperature-size plane. They also illuminate some strong effects of finite-size on quantities which do not diverge at the critical point. They then review Monte Carlo studies for 3 dimensional Ising models of various sizes (L = 2--100) at various temperatures. From these results they find that the data for the renormalized coupling constant collapses nicely when plotted against the correlation length, determined in a system of edge length L, divided by L. They also find that {zeta}{sub L}/L {ge} 0.26 is definitely too large for reliable studies of the critical value, g*, of the renormalized coupling constant. They have reasonable evidence that {zeta}{sub L}/L {approx} 0.1 is adequate for results that are within one percent of those for the infinite system size. On this basis, they have conducted a series of Monte Carlo calculations with this condition imposed. These calculations were made practical by the development of improved estimators for use in the Swendsen-Wang cluster method. The authors found from these results, coupled with a reversed limit computation (size increases with the temperature fixed at the critical temperature), that g* > 0, although there may well be a sharp downward drop in g as the critical temperature is approached in accord with the predictions of series analysis. The results support the validity of hyperscaling in the 3 dimensional Ising model.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 102238
- Report Number(s):
- LA-UR-95-2506; CONF-9507156-1; ON: DE95017012; TRN: AHC29524%%118
- Resource Relation:
- Conference: Hayashibara forum `95, Kyoto (Japan), Jul 1995; Other Information: PBD: [1995]
- Country of Publication:
- United States
- Language:
- English
Similar Records
Continuous-spin Ising model, g/sub 0/:f/sup 4/:/sub d/ field theory, and the renormalization group
Critical exponents for the 3D Ising model