Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)$^*$ and Ising$^*$ continuous transitions
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| Format: | Preprint |
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2024
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| _version_ | 1866912018559139840 |
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| author | Bonati, Claudio Pelissetto, Andrea Vicari, Ettore |
| author_facet | Bonati, Claudio Pelissetto, Andrea Vicari, Ettore |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_13485 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)$^*$ and Ising$^*$ continuous transitions Bonati, Claudio Pelissetto, Andrea Vicari, Ettore High Energy Physics - Lattice Statistical Mechanics 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. |
| title | Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)$^*$ and Ising$^*$ continuous transitions |
| topic | High Energy Physics - Lattice Statistical Mechanics |
| url | https://arxiv.org/abs/2405.13485 |