I will present results on two of my topics of interest. In the first part
we investigate the existence of a stripe-glass phase in a two-dimensional
system with no quenched disorder, which is however frustrated by the
competition of interactions on different length scales. The configurational
entropy is computed through a method applied to frustrated systems with no
quenched disorder, and through a 1/N expansion of the glass free energy.
The stripe-glass phase is connected to the appearance of a finite
off-diagonal replica correlation function, below a crossover temperature,
related to the mobility of defects in the sample. The off-diagonal
correlations in replica space are connected to the asymptotic limit of the
two-times dynamic correlation function. Within this approach we find no
finite contribution for the correlation between distinct replicas, which
results in a vanishing configurational entropy. Therefore, we conclude that
glassiness does not emerge at any temperature in the aforementioned model.

In the second part I will present some results on the ergodicity properties
of the Anderson model defined on the Bethe lattice. Our study is motivated
by the conjectured existence of a phase for intermediary disorder strength
values whose ergodicity properties are distinct from the fully ergodic
extended phase, as well as from the completely ergodicity broken localised
one. This kind of phase is seen to occur on other models such as the
Directed Polymer with random complex weights. For an ensemble of system's
realizations, we have studied eigenvalues and eigenstates statistics
through exact diagonalization. In particular we analysed the neighboring
gaps ratio statistics, the statistics of inverse participation ratios,
including multifractality analysis. We find evidence of the presence of an
intermediary disorder phase whose corresponding statistics are neither
expressing extended nor localised states.