# Exact sampling from non-attractive distributions using summary states

Propp and Wilson's method of coupling from the past allows one to
efficiently generate *exact* samples from attractive statistical
distributions (e.g., the ferromagnetic Ising model). This method may
be generalized to non-attractive distributions by the use of *summary
states*, as first described by Huber. Using this method, we present exact
samples from a frustrated antiferromagnetic triangular Ising model and the
antiferromagnetic *q*=3 Potts model. We discuss the advantages and
limitations of the method of summary states for practical sampling, paying
particular attention to the slowing down of the algorithm at low
temperature. In particular, we show that such a slowing down can occur in
the absence of a physical phase transition.

### Preprint

### Additional data

### Links

Exact sample from the *q*=3 Potts model on a square lattice at
*T*=1.2 with zero applied magnetic field.

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Last modified: Tue Jan 6 18:44:47 2004