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...

This manuscript is a brief summary of a talk designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena—scale invariance and universality—can be useful in guiding research on interpreting empirical data on economic fluctuations....

We empirically quantify the relation between trading activity—measured by the number of transactions N—and the price change G(t) for a given stock, over a time interval [t,t+Δt]. We relate the time-dependent standard deviation of price changes—volatility—to two microscopic quantities:...