  We present iterative Monte Carlo algorithm for which the temperature variable
is attracted by a critical point. The algorithm combines techniques of single
histogram reweighting and linear filtering. The 2d Ising model of ferromagnet
is studied numerically as an illustration. In that case, the iterations
uncovered stationary regime with invariant probability distribution function of
temperature which is peaked nearly the pseudocritical temperature of specific
heat. The sequence of generated temperatures is analyzed in terms of stochastic
autoregressive model. The error of histogram reweighting can be better
understood within the suggested model. The presented model yields a simple
relation, connecting variance of pseudocritical temperature and parameter of
linear filtering.
