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These notes focus on the description of the phases of matter in two dimensions. Firstly, we present a brief discussion of the phase diagrams of bidimensional interacting passive systems, and their numerical and experimental measurements. The presentation will be short and schematic. We will complement these notes with a rather complete bibliography that should guide the students in their study of the development of this very rich subject over the last century. Secondly, we summarise very recent results on the phase diagrams of active Brownian disks and active dumbbell systems in two dimensions. The idea is to identify all the phases and to relate, when this is possible, the ones found in the passive limit with the ones observed at large values of the activity, at high and low densities, and for both types of constituents. Proposals for the mechanisms leading to these phases will be discussed. The physics of bidimensional active systems open many questions, some of which will be listed by the end of the Chapter.
Active matter has been intensely studied for its wealth of intriguing properties such as collective motion, motility-induced phase separation (MIPS), and giant fluctuations away from criticality. However, the precise connection of active materials wi
We study crystal melting in two-dimensional antiferromagnets, by analyzing the statistical mechanics of the six-state clock model on a lattice in which defects (dislocations and disclinations) are allowed to appear. We show that the elementary disloc
We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the basis of t
We compute the shear and bulk viscosities, as well as the thermal conductivity of an ultrarelativistic fluid obeying the relativistic Boltzmann equation in 2+1 space-time dimensions. The relativistic Boltzmann equation is taken in the single relaxati
Collective motion is often modeled within the framework of active fluids, where the constituent active particles, when interactions with other particles are switched off, perform normal diffusion at long times. However, in biology, single-particle su