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gaugePaper.aux
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gaugePaper.aux
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\relax
\citation{Creutz}
\citation{DAdda}
\citation{Rebbi}
\citation{Grosse}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Definitions and QFT background}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Lattice gauge theories}{5}}
\newlabel{gaugeAction}{{1}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Gauge invariance and group theory}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}A note on gauge invariance and partition functions}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Monte Carlo techniques}{7}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Metrics for Monte Carlo}{8}}
\citation{Creutz}
\@writefile{toc}{\contentsline {section}{\numberline {5}Gauge.py}{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces $\mathbb {Z}_2$ lattice gauge theory phase diagram for a 3D lattice.}}{10}}
\newlabel{equilibration}{{1}{10}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Results}{11}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}$\mathbb {Z}_N$}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces $\mathbb {Z}_2$ lattice gauge theory phase diagram for a 2D lattice.}}{11}}
\newlabel{z2,2d}{{2}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces $\mathbb {Z}_2$ lattice gauge theory phase diagram for a 3D lattice.}}{11}}
\newlabel{z2,3d}{{3}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces $\mathbb {Z}_2$ phase diagram for a 4D, 5 by 5 by 5 by 5 lattice. The hysteresis loop betrays a phase transition at around 1.4.}}{12}}
\newlabel{z2,4d}{{4}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces The phase transition region for $\mathbb {Z}_2$ LGT on a 4D, 5 by 5 by 5 by 5 lattice, using the phase boundary method.}}{12}}
\newlabel{z2,4d,phase}{{5}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces $\mathbb {Z}_2$ phase diagram for a 5D, 5 by 5 by 5 by 5 by 5 lattice and for a 6D 5 by 5 by 5 by 4 by 4 by 4 lattice.}}{12}}
\newlabel{z2,56d}{{6}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces $\mathbb {Z}_N$ phase diagrams for a 3D, 7 by 7 by 7 lattice, for various $N$, and for two different types of action.}}{13}}
\newlabel{znactions}{{7}{13}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces $\mathbb {Z}_N$ phase diagrams for a 4D, 7 by 7 by 7 by 7 lattice, for various $N$.}}{14}}
\newlabel{zn,4d}{{8}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces $\mathbb {Z}_N$ capacities for a 4D, 7 by 7 by 7 by 7 lattice, for various $N$. Note the blip on the far right for $\mathbb {Z}_6$: this may be a second phase transition. }}{14}}
\newlabel{heatcapz}{{9}{14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Klein 4-group}{14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.3}Quaternion group}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Phase diagram of $K_4$, compared against $\mathbb {Z}_4$, for a 3D, 7 by 7 by 7 lattice and for a 4D 7 by 7 by 7 by 7 lattice.}}{15}}
\newlabel{k4vz4}{{10}{15}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Phase diagram of Q, compared against $\mathbb {Z}_8$, for a 3D, 7 by 7 by 7 lattice and for a 4D 7 by 7 by 7 by 7 lattice.}}{15}}
\newlabel{qvz8}{{11}{15}}
\bibcite{Creutz}{1}
\bibcite{Munster}{2}
\bibcite{DAdda}{3}
\bibcite{Rebbi}{4}
\bibcite{Grosse}{5}
\bibcite{Billo}{6}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces A cross section of a quaternion LFT on a 3D, 7 by 7 by 7 lattice at $\beta =2$. Different edge colors represent different group elements (black is the identity).}}{16}}
\newlabel{qcrosssection}{{12}{16}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Conclusions}{16}}