extending to low temperatures with no critical points intervening, and no vortex slush.

The difficulty of performing reliable analytical calculations has thus led to numerous numerical investigations,[@Ryu; @Wilkin; @Otterlo; @Reichhardt; @NonoHu; @OTmelt; @OlssonVG; @Kawamura0; @Kawamura; @Lidmar; @DasguptaValls1; @DasguptaValls2] in which one hopes to map out various aspects of the vortex line phase diagram within a well defined simple model. In this paper we report on one such investigation, using the three-dimensional (3D) uniformly frustrated XY model with uncorrelated quenched disorder in the couplings, as a model for a strong type-II superconductor with random point pinning. A virtue of the XY model is that it describes realistic vortex line interactions with no restrictions on vortex line excitations; both overhangs in the field induced vortex lines, and closed thermally excited vortex loops are included. The details of vortex line cores are handled by the short length cutoff of the numerical grid, and hence issues concerning vortex line cutting are treated with a minimum of ad hoc assumptions. Our model holds in the limit of infinite penetration length, $\lambda\to\infty$, and we comment later on the implications of this approximation.

We build upon our earlier work[@OTmelt; @OlssonVG] to present here the equilibrium phase diagram 