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.
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