20 research outputs found
Gibbs-non-Gibbs properties for n-vector lattice and mean-field models
We review some recent developments in the study of Gibbs and non-Gibbs
properties of transformed n-vector lattice and mean-field models under various
transformations. Also, some new results for the loss and recovery of the Gibbs
property of planar rotor models during stochastic time evolution are presented.Comment: 31 pages, 6 figure
Gibbsianness versus Non-Gibbsianness of time-evolved planar rotor models
We study the Gibbsian character of time-evolved planar rotor systems on Z^d,
d at least 2, in the transient regime, evolving with stochastic dynamics and
starting with an initial Gibbs measure. We model the system by interacting
Brownian diffusions, moving on circles. We prove that for small times and
arbitrary initial Gibbs measures \nu, or for long times and both high- or
infinite-temperature measure and dynamics, the evolved measure \nu^t stays
Gibbsian. Furthermore we show that for a low-temperature initial measure \nu,
evolving under infinite-temperature dynamics thee is a time interval (t_0, t_1)
such that \nu^t fails to be Gibbsian in d=2.Comment: latexpdf, with 2 pdf figure
Loss and Recovery of Gibbsianness for XY models in external fields
We consider planar rotors (XY spins) in , starting from an
initial Gibbs measure and evolving with infinite-temperature stochastic
(diffusive) dynamics. At intermediate times, if the system starts at low
temperature, Gibbsianness can be lost. Due to the influence of the external
initial field, Gibbsianness can be recovered after large finite times. We prove
some results supporting this picture.Comment: 14 pages, 2 figure
Discrete approximations to vector spin models
We strengthen a result of two of us on the existence of effective
interactions for discretised continuous-spin models. We also point out that
such an interaction cannot exist at very low temperatures. Moreover, we compare
two ways of discretising continuous-spin models, and show that, except for very
low temperatures, they behave similarly in two dimensions. We also discuss some
possibilities in higher dimensions.Comment: 12 page
Chaotic temperature dependence at zero temperature
We present a class of examples of nearest-neighbour, boubded-spin models, in
which the low-temperature Gibbs measures do not converge as the temperature is
lowered to zero, in any dimension