Events

Date: 16 October 2026   Time: 11:00 - 12:00     

Location: MB-503

In this work, we study the phase transitions of the three-dimensional (q=3) and (q=4) state random-field Potts models (RFPMs). A key universal feature of these systems is that their phase transitions are governed by a zero-temperature random fixed point. We investigate their critical behaviour by determining the ground states at temperature T = 0. Since finding exact ground states of the RFPM is known to be an NP-hard problem, we employ a recently developed quasi-exact scheme based on graph cuts to determine approximate ground states and investigate the critical behaviour associated with the zero-temperature random fixed point.

We calculate several key observables, including the magnetisation, Binder cumulant, energy cumulant, specific heat, and connected and disconnected susceptibilities, and extrapolate them towards the quasi-exact limit. By analysing systems of different sizes, we perform an extensive finite-size scaling analysis to estimate the critical points and characterise the magnetic ordering transitions. In contrast to the corresponding pure systems, in which both the q =3 and q = 4 Potts models exhibit first-order phase transitions, we find compelling evidence that the transitions become continuous in the presence of random fields. We determine the critical exponents with high precision and find that they differ from those of the random-field Ising model (RFIM), suggesting distinct universality classes for the RFPMs with different values of q. Nevertheless, both the RFPM and the RFIM are found to obey a two-exponent scaling scenario.