TIME-DEPENDENT STATISTICS OF THE ISING MODEL
Journal Article
·
· Journal of Mathematical Physics (New York) (U.S.)
The individual spins of the Ising model are assumed to interact with an external agency (e.g., a heat reservoir) that causes them to change their states randomly with time. Coupling between the spins is introduced through the assumption that the transition probabilities for any one spin depend on the values of the neighboring spins. This dependence is determined, in part, by the detailed balancing condition obeyed by the equilibrium state of the model. The Markoff process that describes the spin functions is analyzed in detail for the case of a closed Nmember chain. The expectation values of the individual spins and of the products of pairs of spins, each of the pair evaluated at a different time, are found explicitiy. The influence of a uniform, time-varying magnetic field upon the model is discussed, and the frequency-dependent magnetic susceptibility is found in the weak-field limit. Some fluctuation-dissipation theorems are derived that relate the susceptibility to the Fourier transform of the time-dependent correlation function of the magnetization at equilibrium. (auth)
- Research Organization:
- Harvard Univ., Cambridge, Mass.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-17-020694
- OSTI ID:
- 4695172
- Journal Information:
- Journal of Mathematical Physics (New York) (U.S.), Journal Name: Journal of Mathematical Physics (New York) (U.S.) Vol. Vol: 4; ISSN JMAPA
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
Similar Records
Monte Carlo Study of the Effect of Initial States and Structural Defects on Nonequilibrium Critical Behavior of the Three-Dimensional Ising Model
Analysis of the Effect of Different Initial States and Structural Defects on the Characteristics of the Nonequilibrium Critical Behavior of the 3D Ising Model
Frustration Properties of the 1D Ising Model
Journal Article
·
Fri Jun 15 00:00:00 EDT 2018
· Physics of the Solid State
·
OSTI ID:22770968
Analysis of the Effect of Different Initial States and Structural Defects on the Characteristics of the Nonequilibrium Critical Behavior of the 3D Ising Model
Journal Article
·
Thu Dec 14 23:00:00 EST 2017
· Journal of Experimental and Theoretical Physics
·
OSTI ID:22756159
Frustration Properties of the 1D Ising Model
Journal Article
·
Wed May 15 00:00:00 EDT 2019
· Journal of Experimental and Theoretical Physics
·
OSTI ID:22917741