On the Logarithmic Triviality of Scalar Quantum Electrodynamics

TL;DR

This study uses lattice simulations to demonstrate the logarithmic triviality of scalar quantum electrodynamics, showing that it behaves like a mean-field theory with second order critical points and no first order transitions.

Contribution

It provides numerical evidence for the logarithmic triviality of scalar QED using finite size scaling and histogram methods on lattice simulations.

Findings

Logarithmic growth of specific heat peaks with lattice size.

Identification of a line of second order critical points.

Correlation length exponent consistent with mean field theory.

Abstract

Using finite size scaling and histogram methods we obtain numerical results from lattice simulations indicating the logarithmic triviality of scalar quantum electrodynamics, even when the bare gauge coupling is chosen large. Simulations of the non-compact formulation of the lattice abelian Higgs model with fixed length scalar fields on $L^{4}$ lattices with $L$ ranging from $6$ through $20$ indicate a line of second order critical points. Fluctuation-induced first order transitions are ruled out. Runs of over ten million sweeps for each $L$ produce specific heat peaks which grow logarithmically with $L$ and whose critical couplings shift with $L$ picking out a correlation length exponent of $0.50(5)$ consistent with mean field theory. This behavior is qualitatively similar to that found in pure $\lambda\phi^{4}$.