ar X iv : q ua nt - p h / 99 05 08 9 v 1 2 6 M ay 1 99 9 EXACT CLASSICAL EFFECTIVE POTENTIALS

A quantum spin system can be modelled by an equivalent classical system, with an effective Hamiltonian obtained by integrating all non-zero frequency modes out of the path integral. The effective Hamiltonian H eff ({S i }) derived from the coherent-state integral is highly singular: the quasiprobability density exp(−βH eff), a Wigner function, imposes quantisation through derivatives of delta functions. This quasiprobability is the distribution of the time-averaged lower symbol of the spin in the coherent-state integral. We relate the quantum Monte Carlo minus-sign problem to the non-positivity of this quasiprobability, both analytically and by Monte Carlo integration.