  Equilibrium systems evolve according to Detailed Balance (DB). This principe
guided development of the Monte-Carlo sampling techniques, of which
Metropolis-Hastings (MH) algorithm is the famous representative. It is also
known that DB is sufficient but not necessary. We construct irreversible
deformation of a given reversible algorithm capable of dramatic improvement of
sampling from known distribution. Our transformation modifies transition rates
keeping the structure of transitions intact. To illustrate the general scheme
we design an Irreversible version of Metropolis-Hastings (IMH) and test it on
example of a spin cluster. Standard MH for the model suffers from the critical
slowdown, while IMH is free from critical slowdown.
