Fluctuation dynamics of the Ising two-dimensional spin model

The fundamental problem of correlation between a catastrophic structural ch ange and the noise parameters of the system was studied. Computer simulatio ns showed the spectral parameters of noise to be correlated with instabilit y of the Ising system. The earliest signals of the forthcoming phase transi tion were analyzed. The Monte Carlo method was applied to simulate the stoc hastic spin kinetics of the two-dimensional (50 x 50) Ising model in the ab sence of an external magnetic field at various ratios between temperature a nd the exchange integral. Transitions of two types were observed, namely, d emagnetization when the system approached the critical temperature and a fl uctuation transition between two metastable states of the system with oppos itely directed total magnetic moments. The time series of total magnetizati on were analyzed, and the power spectra, structure functions, and distribut ion functions for various temperatures were obtained. The spectral characte ristics were shown to be more sensitive to changes in the phase state of sy stems and to give earlier indications of forthcoming phase changes than ave rage statistical parameters. The parameters obtained from an analysis of po wer spectra In S(f) and structure functions phi ((2))(tau) (time of memory loss and spectral power at low frequencies) were close to each other.