Critical nonequilibrium relaxation in cluster algorithms in the BKT and weak first-order phase transitions

Recently we showed that the critical nonequilibrium relaxation in cluster algorithms is widely described by the stretched-exponential decay of physical quantities in the Ising [1] or Heisenberg [2] models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless (BKT) phase transition in the 2D XY model (simple exponential decay) and in the weak first-order phase transition in the 2D $q=5$ Potts model (power-law decay) [3], which means that these phase transitions can clearly be characterized by the present analysis. These relaxation behaviors are compared with those in the 3D and 4D XY models (second-order phase transition) and in the 2D $q$-state Potts models ($2 \le q \le 4$ for second-order and $q \ge 6 $ for strong first-order phase transitions. \smallskip \par \noindent [1] Y.~Nonomura, J.\ Phys.\ Soc.\ Jpn.\ {\bf 83}, 113001 (2014); [2] Y.~Nonomura and Y.~Tomita, arXiv:1508.05218; [3] Y.~Nonomura and Y.~Tomita, arXiv:1509.08352.