Euler method versus RK45?

[WeileiZeng]

In the code, the Euler method with fixed step length is implemented as the solver for the master equation. Why Runge Kutta method with 4th order accuracy and adjustable step length not provide a higher accuracy?

This is mentioned in the paper but I haven't get the point.

In my impression, when the system reach the bifurcation point, most spins start moving towards a stable solution, with a very small momentum. This process takes time. A more accurate solver with smaller step length should be helpful in this procedure, reducing random flips by noise and speeding up stabilizing the system.