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Here is the circuit in question: https://www.circuitlab.com/circuit/nju7nfp5mvu3/constant-current-circuit/

The output current at the load (R4) is simulated to be a bipolar current, when it isn't possible for current to flow through the MOSFET in the reverse direction due to the unipolar source used (V3). Other simulators such as the Falstad siulator and LTSpice show a correct unipolar current as output.

See discussion here for more details, as well as an image of the simulation output: https://www.reddit.com/r/AskElectronics/comments/5uc1pc/why_does_a_spike_occur_in_the_current_when_it/

Is this an error in the parameters of the IRF1530 or in a way that it is being simulated?

any thoughts?

I think what's going wrong is that your opamp has unbounded outputs. If you plot the gate voltage, you'll see what I mean!

Try replacing your opamp with the opamp with rails model, powered by +5 and GND rails.