In this paper we investigate the Hamiltonian dynamics of a lattice gauge
model in three spatial dimension. Our model Hamiltonian is defined on the basis
of a continuum version of a duality transformation of a three dimensional Ising
model. The system so obtained undergoes a thermodynamic phase transition in the
absence of symmetry-breaking. Besides the well known use of quantities like the
Wilson loop we show how else the phase transition in such a kind of models can
be detected. It is found that the first order phase transition undergone by
this model is characterised according to an Ehrenfest-like classification of
phase transitions applied to the configurational entropy. On the basis of the
topological theory of phase transitions, it is discussed why the seemingly
divergent behaviour of the third derivative of configurational entropy can be
considered as the "shadow" of some suitable topological transition of certain
submanifolds of configuration space.Comment: 31 pages, 9 figure
