Equilibration Why Wait

As a practical matter, one cannot immediately start accumulating U and for the computation of averages. The MMC algorithm does not instantly 

In these plots the thermodynamic quantities go through some initial transient behavior, and then eventually settle down into small-amplitude oscillations. At this very low temperature both U and Cy settle down rapidly and they do so on similar timescales. Typically, the running averages of U and Cy will not converge simultaneously. In fact Cy will usually be the slower of the two to converge, since its fluctuations arise from fluctuations of the 

Note that if a different choice of initial conditions is used (e.g., starting from a lattice configuration rather than from a random one), eq might need to be adjusted (up or down). It is advisable to do a new equilibration study each time one substantially alters the way things are done, or when the system s properties become significantly different (e.g., when one moves substantially above or below a melting transition). 

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