伊辛规范理论中的复制希格斯场：配列序
Replicating Higgs fields in Ising gauge theory: the registry order
AI总结：
本研究在耦合多份希格斯物质拷贝的$Z_2$规范场论中发现新的配列序参量，通过蒙特卡洛模拟揭示其起源于规范场通量介导的相互作用，并发现不同理论相图存在伪普适性，规范场动力学起主导作用。
摘要：
我们考虑耦合“希格斯”物质场的$Z_2$规范场论，引入多份此类物质拷贝，它们完全通过规范场相互作用，涉及$Z_2 \times Z_2 \times Z_2\cdots / Z_2$和$O(N) \times O(N) \times O(N) \cdots / Z_2$理论族。我们发现这类理论的希格斯相由一种此前未被识别的“配列（registry）”序参量表征。该序参量具有规范不变的$p = 2^{N_{\text{rep}}}/2$型Potts（波茨）对称性，其中$N_{\text{rep}}$为物质拷贝数。这种配列的含义是，不同物质拷贝的矢量在局域上严格以平行或反平行方式排列，即便在连续$O(2)$对称性的情况下也是如此。借助Monte-Carlo（蒙特卡洛）模拟的支持，我们将这种配列序的起源归因于与$Z_2$规范场相关的通量（“vison，涡旋子”）介导的规范相互作用，它在由规范不变的整体对称性控制的有效序参量理论中间接施加了离散对称性。此外，我们的模拟还揭示了一种此前未被识别的“伪普适性”，它与各类理论整体相图极为相似的形式相关，表明动力学的规范场部分发挥了显著的“主导”作用。
英文摘要：
We consider $Z_2$ gauge field theory coupled to "Higgs" matter fields invoking several copies of such matter, interacting entirely through the gauge fields, the $Z_2 \times Z_2 \times Z_2\cdots / Z_2$ and the $O(N) \times O(N) \times O(N) \cdots / Z_2$ families of theories. We discover that the Higgs phase of such theories is characterized by a hitherto unidentified "registry" order parameter. This is characterized by a gauge invariant $p = 2^{N_{\text{rep}}}/2$ Potts type symmetry where $N_{\text{rep}}$ is the number of matter copies. The meaning of this registry is that the different matter copies align their vectors locally in strictly parallel or anti-parallel fashion, even dealing with the continuous $O(2)$ symmetry. Supported by Monte-Carlo simulations, we identify the origin of this registry order in terms of the gauge interactions mediated by the fluxes ("visons") associated with the $Z_2$ gauge fields, indirectly imposing the discrete symmetry in the gauge invariant global symmetry controlled effective order parameter theory. In addition, it appears that our simulations reveal a hitherto unidentified "pseudo-universality" associated with the very similar form of the overall phase diagrams of the various theories suggesting a remarkable "governance" by the gauge field part of the dynamics.
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