deletions | additions       diff --git a/Magnetic response.tex b/Magnetic response.tex  index c922dac..627a01b 100644  --- a/Magnetic response.tex  +++ b/Magnetic response.tex 
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second one is the Zeeman term that represents the coupling of the  electronic spin with the magnetic field.  As our main interest is the evaulation evaluation  of the magnetic susceptibility, in the following we consider a perturbative uniform static magnetic  field \(\vec{B}\) and zero total spin. In the Coulomb gauge the  corresponding vector potential, \(\vec{A}\), is given as 
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\end{equation}  Unfortunately, the integration path can be any one that connects the two  points \(\vec{r}\) and \(\vec{r}'\), so an infinite number of choices  is possible, each yielding slightly different results for the magentic magnetic  properties. There are two different integration paths that have been  used in the literature. The first was proposed by Ismail-Beigi,  Chang, and Louie (ICL) in 2001\cite{Ismail_Beigi_2001} and gives the