Abstract

Long-range translational order is forbidden in low dimensional systems with short-range interactions, and solid phases only have quasi long-range translational order in two dimensions. A mechanism for the transition from solid to liquid led by the dissociation of dislocation pairs was proposed by Kosterlitz & Thouless in their 1972 & 1973 Nobel prize papers. Knowing that long-range orientational order is possible in two dimensions, Nelson, Halperin and Young argued that the transition actually occurs in two steps, the second one being triggered by the unbinding of disclinations. In this picture the intermediate phase keeps quasi long-range orientational order, and the two transitions are of infinite order. Based on simulations of hard disks, Bernard & Krauth recently contested the latter picture. In this talk I will briefly review all these issues and I will extend their analysis to systems of self-propelled particles, the constituents of active matter, a new kind of soft matter relevant to describe numerous biological problems. In particular, I will discuss in detail the phase diagram of active Brownian particles and the role played by topological effects in all the transitions found.

The references are

Clustering of topological defects in two-dimensional melting of active and passive disks Pasquale Digregorio, Demian Levis, Leticia F. Cugliandolo, Giuseppe Gonnella, Ignacio Pagonabarraga arXiv:1911.06366

Full phase diagram of active Brownian disks: from melting to motility-induced phase separation Pasquale Digregorio, Demian Levis, Antonio Suma, Leticia F. Cugliandolo, Giuseppe Gonnella, Ignacio Pagonabarraga arXiv:1805.12484, Phys. Rev. Lett. 121, 098003 (2018)