Direction-sweep Markov chains

We discuss a non-reversible, lifted Markov-chain Monte Carlo (MCMC) algorithm for particle systems in which the direction of proposed displacements is changed deterministically. This sweeps through directions analogously to popular MCMC sweep methods or spin indices. Direction-sweep can be applied wide range original reversible non-reversible Markov chains, such as Metropolis event-chain algorithm. For single two-dimensional dipole, we consider direction-sweep limit where restricted equilibrium reached among accessible configurations before changing direction. show rigorously that leaves stationary probability distribution unchanged, and it profoundly modifies trajectory. Long excursions, with persistent rotation one direction, alternate long sequences rapid zigzags resulting opposite small increments. The mapping Langevin equation then yields exact scaling excursions while are described non-linear differential solved exactly. have shorter mixing times than algorithms random updates directions. point out possible applications polymer physics molecular simulation.