Bayesian phase transition for the critical Ising model: Enlarged replica symmetry in the epsilon expansion and in 2D
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| Format: | Preprint |
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2026
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| _version_ | 1866918468099506176 |
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| author | Wiese, Kay Joerg Das, Alapan Nahum, Adam |
| author_facet | Wiese, Kay Joerg Das, Alapan Nahum, Adam |
| contents | A process that images or measures bond energies in the critical Ising model can be in distinct measurement ``phases'', depending on the precision of measurement. We study the transition into the strong-measurement phase using replica field theory (an epsilon expansion around six dimensions) and numerical simulations in two dimensions. The results reveal multiscaling of correlation functions at the critical point, and a striking enlarged symmetry of the replica description. This is an analog of the Nishimori phenomenon in the Ising spin glass, in a distinct replica limit. The enlarged symmetry is present microscopically for certain measurement protocols, but more generally can emerge in the infrared, and it fixes the exact value of the exponent for the Edwards-Anderson correlator both in 2D and near the upper critical dimension. We also examine the epsilon expansion for models with power-law interactions and/or long-range measurement. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_23346 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian phase transition for the critical Ising model: Enlarged replica symmetry in the epsilon expansion and in 2D Wiese, Kay Joerg Das, Alapan Nahum, Adam Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Data Analysis, Statistics and Probability Quantum Physics A process that images or measures bond energies in the critical Ising model can be in distinct measurement ``phases'', depending on the precision of measurement. We study the transition into the strong-measurement phase using replica field theory (an epsilon expansion around six dimensions) and numerical simulations in two dimensions. The results reveal multiscaling of correlation functions at the critical point, and a striking enlarged symmetry of the replica description. This is an analog of the Nishimori phenomenon in the Ising spin glass, in a distinct replica limit. The enlarged symmetry is present microscopically for certain measurement protocols, but more generally can emerge in the infrared, and it fixes the exact value of the exponent for the Edwards-Anderson correlator both in 2D and near the upper critical dimension. We also examine the epsilon expansion for models with power-law interactions and/or long-range measurement. |
| title | Bayesian phase transition for the critical Ising model: Enlarged replica symmetry in the epsilon expansion and in 2D |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Data Analysis, Statistics and Probability Quantum Physics |
| url | https://arxiv.org/abs/2604.23346 |