Multicritical point of the three-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> gauge Higgs model

We investigate the multicritical behavior of three-dimensional Z_2 gauge Higgs model, at point (MCP) its phase diagram, where one first-order transition line and two continuous Ising-like lines meet. The duality properties model determine some features MCP located along self-dual line. Moreover, we argue that system develops a XY MCP, which is controlled by stable fixed Landau-Ginzburg-Wilson field theory with competing scalar fields associated meeting MCP. This implies an effective enlargement symmetry modes to group O(2). also provide numerical results support scenario.