XIIth Brazilian School of Probability

Aernout van Enter (Rijksuniversity Groningen)

Loss and recovery of temperature during fast heating:
Conservation, loss and recovery of the Gibbs property in Ising and XY models.

We study a Gibbs measure at a certain temperature, subject to a stochastic evolution (spin-flip for Ising spins, spin diffusion for XY spins), which has an invariant measure at a different (high or infinite) temperature. We present various results about when the evolved measure in the transient regime can be written as a Gibbs measure for some effective interaction. The norm of such an inverse interaction has an interpretation as an inverse temperature.

Loss and recovery of temperature during fast heating:
Conservation, loss and recovery of the Gibbs property in Ising and XY models.

We study a Gibbs measure at a certain temperature, subject to a stochastic evolution (spin-flip for Ising spins, spin diffusion for XY spins), which has an invariant measure at a different (high or infinite) temperature. We present various results about when the evolved measure in the transient regime can be written as a Gibbs measure for some effective interaction. The norm of such an inverse interaction has an interpretation as an inverse temperature.