Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)$^*$ and Ising$^*$ continuous transitions
| Autor: | Bonati, Claudio, Pelissetto, Andrea, Vicari, Ettore |
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| Rok vydání: | 2024 |
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| Zdroj: | Phys. Rev. B 110, 125109 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.110.125109 |
| Popis: | We study the O($N$)$^*$ transitions that occur in the 3D $\mathbb{Z}_2$-gauge $N$-vector model, and the analogous Ising$^*$ transitions occurring in the 3D $\mathbb{Z}_2$-gauge Higgs model, corresponding to an $N$-vector model with $N=1$. At these transitions, gauge-invariant correlations behave as in the usual $N$-vector/Ising model. Instead, the nongauge invariant spin correlations are trivial and therefore the spin order parameter that characterizes the spontaneous breaking of the O($N$) symmetry in standard $N$-vector/Ising systems is apparently absent. We define a novel gauge fixing procedure -- we name it stochastic gauge fixing -- that allows us to define a gauge-dependent vector field that orders at the transition and is therefore the appropriate order parameter for the O($N$) symmetry breaking. To substantiate this approach, we perform numerical simulations for $N=3$ and $N=1$. A finite-size scaling analysis of the numerical data allows us to confirm the general scenario: the gauge-fixed spin correlation functions behave as the corresponding functions computed in the usual $N$-vector/Ising model. The emergence of a critical vector order parameter in the gauge model shows the complete equivalence of the O($N$)$^*$/Ising$^*$ and O($N$)/Ising universality classes. Comment: 15 pages, 16 pdf figures, minor changes |
| Databáze: | arXiv |
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