We compute the internal energy of different Ising type models, both long–range and short–range, under Tsallis statistics using the microcanonical and the canonical ensembles and we discuss under which conditions both ensembles give equivalent results.

6 0 5 10 15 20 s s s s s s s s s s s s s s s s s s s Figure 1: correlation lengths ~ L (empty dots) and L (full dots) at the RSB transition for diierents lattice sizes L.

We study disk amplitudes whose boundaries have heterogeneous matter states in a system of (4, 5) conformal matter coupled to 2-dim gravity. They are analysed by using the 3-matrix chain model in the large N limit. Each of the boundaries is composed of two or three parts with distinct matter states. From the obtained amplitudes, it turns out that each heterogeneous boundary loop splits into seve...

Continuing our work [12], where a explicit formula for the two-point functions of the two dimensional Z-invariant Ising model were found. I obtain here different results for the higher correlation functions and several consistency checks are done.