  We study a gauge/gravity model for the thermodynamics of a gauge theory with
one running coupling. The gravity side contains an ansatz for the metric and a
scalar field, on the field theory side one starts by giving an ansatz for the
beta function describing the scale dependence of the coupling. The model is
based on relating the scale to the extra dimensional coordinate and the beta
function to the gravity fields, thereby also determining the scalar field
potential. We study three different forms of beta functions of increasing
complexity and give semianalytic solutions describing first order or continuous
transitions.
