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The integer quantum Hall states at fillings $\nu = 0$ and $|\nu| = 1$ inmonolayer graphene have drawn much attention as they are generated byelectron-electron interactions. Here we explore aspects of the $\nu = 0$ and$|\nu| = 1$ quantum Hall states relevant for experimental samples. Inparticular, we study the effects of finite extent and finite temperature on the$\nu = 0$ state and finite temperature for the $\nu = 1$ state. For the $\nu =0$ state we consider the situation in which the bulk is a cantedantiferromagnet and use parameters consistent with measurements of the bulk gapto study the edge states in tilted magnetic fields in order to compare withexperiment [A. F. Young et al., Nature 505, 528 (2014)]. When spatialmodulation of the order parameters is taken into account, we find that forgraphene placed on boron nitride, the gap at the edge closes for magneticfields comparable to those in experiment, giving rise to edge conduction with$G \sim 2e^2/h$ while the bulk gap remains almost unchanged. We also study thetransition into the ordered state at finite temperature and field. We determinethe scaling of critical temperatures as a function of magnetic field, $B$, anddistance to the zero field critical point and find sublinear scaling withmagnetic field for weak and intermediate strength interactions, and $\sqrt{B}$scaling at the coupling associated with the zero field quantum critical point.We also predict that critical temperatures for $\nu = 0$ states should be anorder of magnitude higher than those for $|\nu| = 1$ states, consistent withthe fact that the low temperature gap for $\nu = 0$ is roughly an order ofmagnitude larger than that for $|\nu| = 1$.

Interacting quantum Hall states in a finite graphene flake and at finite temperature