Sorry, perhaps I did not explain myself :)
One can see the phase oscillates between -\pi and \pi.
I would like to compute how many times the phase changes by 2\pi as one 
goes around the origin. 

On Wednesday, February 4, 2015 at 1:31:53 AM UTC+1, Steven G. Johnson wrote:
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>
>
> On Tuesday, February 3, 2015 at 1:17:15 PM UTC-5, Andrei Berceanu wrote:
>
>> How can I numerically compute the total change in phase as one goes 
>> around a closed loop centered on the site $m=n=0$?
>>
>
> Seems like
>
>     totalchangeinphase(m,n) = 0
>
> would work and be very efficient.   (As you described your problem, your 
> phase sounds like a single-valued function of m & n, hence the total change 
> around any closed loop would be zero.  Unless you mean something different 
> by "total change"?)
>

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