Character Expansion, Zeros of Partition Function and $θ$-term in U(1) Gauge Theory

Details Character Expansion, Zeros of Partition Function and $θ$-term in U(1) Gauge Theory Character Expansion, Zeros of Partition Function and $θ$-term in U(1) Gauge Theory

1995-08-09

arxiv.org/abs/hep-lat/9508011v1

Prog.Theor.Phys. 94 (1995) 861-872

Physics

High Energy Physics

High Energy Physics - Lattice

14 pages, plaintex, 4 figures

Scientific paper

10.1143/PTP.94.861

Character expansion developed in real space renormalization group (RSRG) approach is applied to U(1) lattice gauge theory with $\th$-term in 2 dimensions. Topological charge distribution $P(Q)$ is shown to be of Gaussian form at any $\b$(inverse coupling constant). The partition function $Z(\th)$ at large volume is shown to be given by the elliptic theta function. It provides the information of the zeros of partition function as an analytic function of $\ze= e^{i \th}$ ($\th$ = theta parameter). These partition function zeros lead to the phase transition at $\th=\pi$. Analytical results will be compared with the MC simulation results. In MC simulation, we adopt (i)``set method" and (ii)``trial function method".

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