Multicritical point of the three-dimensional Z2 gauge Higgs model

Abstract

We investigate the multicritical behavior of the three-dimensional ${\mathbb{Z}}_{2}$ gauge Higgs model at the multicritical point (MCP) of its phase diagram, where one first-order transition line and two continuous Ising-like transition lines meet. The duality properties of the model determine some features of the multicritical behavior at the MCP located along the self-dual line. Moreover, we argue that the system develops a multicritical $XY$ behavior at the MCP, which is controlled by the stable $XY$ fixed point of the three-dimensional multicritical Landau-Ginzburg-Wilson field theory with two competing scalar fields associated with the continuous ${\mathbb{Z}}_{2}$ transition lines meeting at the MCP. This implies an effective enlargement of the symmetry of the multicritical modes at the MCP to the continuous group O(2). We also provide numerical results to support the multicritical $XY$ scenario.