We present extensive numerical simulations of a generalized XY model with nematic-like terms recently proposed by Poderoso et al [PRL 106(2011)067202]. Using finite size scaling and focusing on the q = 3 case, we locate the transitions between the paramagnetic (P), the nematic-like (N) and the ferromagnetic (F) phases. The results are compared with the recently derived lower bounds for the P-N and P-F transitions. While the P-N transition is found to be very close to the lower bound, the P-F transition occurs significantly above the bound. Finally, the transition between the nematic-like and the ferromagnetic phases is found to belong to the 3-states Potts universality class.

We study a generalization of the XY model with an additional nematic-like term through extensive numerical simulations and finite-size techniques, both in two and three dimensions. While the original model favors local alignment, the extra term induces angles of 2π/q between neighboring spins. We focus here on the q = 8 case (while presenting new results for other values of q as well) whose phase diagram is much richer than the well-known q = 2 case. In particular, the model presents not only continuous, standard transitions between Berezinskii-Kosterlitz-Thouless (BKT) phases as in q = 2, but also infinite-order transitions involving intermediate, competition-driven phases absent for q = 2 and 3. Besides presenting multiple transitions, our results show that having vortices decoupling at a transition is not a sufficient condition for it to be of BKT type.

When the interactions between cooperators (C) and defectors (D) can be partially avoided within a population, there may be an overall enhancement of cooperation. One example of such screening mechanism occurs in the presence of risk-averse agents (loners, L) that are neutral towards others, i.e., both L and its opponent, whatever its strategy, receive the same payoff. Their presence in the Prisoner's Dilemma (PD) game sustains the coexistence of cooperators and defectors far beyond the level attained in their absence. Another screening mechanism is a heterogeneous landscape obtained, for example, by site diluting the lattice. In this case, cooperation is enhanced with some fraction of such inactive, interaction-averse sites. By considering the interplay of both mechanisms, we show that there is an explosive increase in the range of densities, just above the percolation threshold, where neutrality is prevented and loners become extinct, the behavior reverting to the pure PD game. Interestingly, this occurs despite defectors being usually abundant in that region. This has to be compared with the corresponding loner-free region in the undiluted case that, besides being very small, is dominated by cooperators.