标题： 标量量子电动力学的相位和平凡性 显示英文标题

标题： The Phases and Triviality of Scalar Quantum Electrodynamics

摘要： 利用格点规范理论技术研究了纯数量规范场论的相图和临界行为。 格点作用量固定标量场（“希格斯”场）的长度，并将规范场当作非紧致场处理。 相图是二维的。 不需要精细调节或外推来研究理论的临界行为。 发现了两条二阶相变线，并通过有限大小标度方法在从$6^4$到$24^4$的不同格点尺寸上研究了每条线的标度律。 一条线对应单极子渗透，另一条线对应“希格斯”相和“库仑”相之间的转变，用发散的比热容来标记。 这些转变线在相图内部相交，似乎没有关联。 单极子渗透转变具有与普通四维无相互作用渗透一致的临界指数。 有限大小标度和直方图方法表明，“希格斯-库仑”转变线上的比热容可以用标量量子电动力学是对数平凡的假设很好地拟合。 这些对数既出现在比热峰的有限大小标度随体积的变化中，也出现在固定但较大的格点上测量的比热容随耦合常数的变化中。 该理论看起来在定性上类似于$\lambda\phi^{4}$。 标准的CRAY随机数生成器RANF被证明是不够的。 显示英文摘要

摘要： The phase diagram and critical behavior of scalar quantum electrodynamics are investigated using lattice gauge theory techniques. The lattice action fixes the length of the scalar (``Higgs'') field and treats the gauge field as non-compact. The phase diagram is two dimensional. No fine tuning or extrapolations are needed to study the theory's critical behovior. Two lines of second order phase transitions are discovered and the scaling laws for each are studied by finite size scaling methods on lattices ranging from $6^4$ through $24^4$. One line corresponds to monopole percolation and the other to a transition between a ``Higgs'' and a ``Coulomb'' phase, labelled by divergent specific heats. The lines of transitions cross in the interior of the phase diagram and appear to be unrelated. The monopole percolation transition has critical indices which are compatible with ordinary four dimensional percolation uneffected by interactions. Finite size scaling and histogram methods reveal that the specific heats on the ``Higgs-Coulomb'' transition line are well-fit by the hypothesis that scalar quantum electrodynamics is logarithmically trivial. The logarithms are measured in both finite size scaling of the specific heat peaks as a function of volume as well as in the coupling constant dependence of the specific heats measured on fixed but large lattices. The theory is seen to be qualitatively similar to $\lambda\phi^{4}$. The standard CRAY random number generator RANF proved to be inadequate