Before revision: We consider Gibbs distributions , which are families of probability distributions over a discrete space \Omega with probability mass function of the form \mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)} for \beta in an interval [\min, \max] and H( \omega ) \in \{0 \} \cup [1, n].
After revision: We consider Gibbs distributions , which are families of probability distributions over a discrete space \Omega with probability mass function of the form \mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)} for \beta in an interval [\min, \max] and H( \omega ) \in \{0 \} \cup [1, n].