Dimensional reduction by Monte Carlo

A Monte Carlo method for mapping a field theoretical or statistical system to a new theory embedded in a space-time of lesser dimensionality is presented. Typically, the critical properties of the dimensionally reduced system depend upon the details of the mapping. As an example, the two-dimensional Ising model is mapped to a one-dimensional Ising model with long-range forces and a phase transition. Systems with long-range interactions and known exponents can thus be constructed with this procedure.