good agreement with recent experiments.[@Pasquini; @Soibel]

The remainder of this paper is organized as follows. In Sec. II we define our model and the quantities we use to map out the phase diagram. In Sec. III we present our results for vortex lattice melting in the limit of weak pinning strengths. In Sec. IV we present our results for the vortex glass at strong pinning strengths. In Sec. V we discuss the smearing of the vortex lattice melting transition at intermediate pinning strengths. In Sec. VI we summarize our results and discuss their relation to other recent numerical works.

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Model {#smodel}
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The model we simulate is the uniformly frustrated 3D XY model, given by the Hamiltonian,[@YHLi] $${\cal H}[\theta({\bf r}_i)]=-\sum_{i\mu}J_{i\mu}\cos(\theta({\bf r}_i)-\theta({\bf r}_i+\hat\mu)-A_{i\mu})\enspace,
\label{eH}$$ which serves as a discretized approximation to the Ginzburg-Landau free energy functional in the London approximation of fixed wavefunction amplitude, and captures the kinetic energy of the flowing supercurrents in the system. Here $\theta({\bf r}_i)$ is the thermally fluctuating phase angle of the superconducting wavefunction on site ${\bf r}_i$ of a cubic $L\times L\times L_z $ grid of sites with bonds in directions $\hat\mu=\hat x,\hat y,\hat z$. $J_{i\mu}$ is the superconducting coupling constant on bond $(i\mu)$ 