A self-adjusted Monte Carlo simulation as a model for financial markets with central regulation

Properties of the self-adjusted Monte Carlo algorithm applied to 2d Ising ferromagnet are studied numerically. The endogenous feedback form expressed in terms of the instant running averages is suggested in order to generate a biased random walk of the temperature that converges to criticality without an external tuning. The robustness of a stationary regime with respect to partial accessibility of the information is demonstrated. Several statistical and scaling aspects have been identified which allow to establish an alternative spin lattice model of the financial market. It turns out that our model alike model suggested by Bornholdt [Int. J. Mod. Phys. C 12 (2001) 667], may be described by Lévy-type stationary distribution of feedback variations with unique exponent α1 3.3. However, the differences reflected by Hurst exponents suggest that resemblances between the studied models seem to be non-trivial.