Computer simulations of three-dimensional classical Heisenberg models
With the aid of large-scale computer simulations on state-of-the-art supercomputers, the author has carried out a comprehensive study of first-order phase transitions, both static and dynamic critical behavior, as well as various excitations in different three-dimensional classical Heisenberg magnetic models with periodic boundary conditions and only nearest-neighbor interactions. In the Monte Carlo study of finite-size effects on the first-order phase transition in the simple-cubic classical Heisenberg ferromagnet, the author found that the current Fisher-Privman theory failed at temperatures close to criticality and/or for small systems. Explicit scaling functions were rederived for the longitudinal magnetization and susceptibility under a new phenomenological assumption. The predictions were in excellent agreement with Monte Carlo simulations. Using both recently developed cluster algorithm and histogram methods, a high-resolution Monte Carlo study of static critical properties of the simple-cubic and body-centered-cubic ferromagnets was performed. From finite-size scaling behavior of various thermodynamic quantities, the inverse critical temperatures were estimated to be 0.693035(37) for the simple-cubic system and 0.486798(12) for the body-centered-cubic system. Estimated static critical exponents for both systems agreed with each other within their respective error bars, and the mean estimates {nu} = 0.7048(30) and {gamma} = 1.3873(85) were also in excellent agreement with field theoretic predictions. Using spin dynamics methods, extensive simulations were carried out of the dynamic critical behavior of the body-centered-cubic ferromagnet. The space-and time-displaced spin-spin correlation functions and their space-time Fourier transforms were calculated to determine neutron- scattering functions.
- Research Organization:
- Georgia Univ., Athens, GA (United States)
- OSTI ID:
- 39302
- Country of Publication:
- United States
- Language:
- English
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