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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.25946 |
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| _version_ | 1866918521723682816 |
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| author | Sun, Yihua Fan, Yuchen |
| author_facet | Sun, Yihua Fan, Yuchen |
| contents | Identifying the asymptotic criticality of a critical endpoint is challenging, as pseudo-first-order signatures persist over accessible system sizes and mask its underlying critical nature. This ambiguity is amplified at endpoints controlled by a marginally irrelevant scaling field, where logarithmic flow delays the onset of asymptotic scaling. Here we develop a generalized field-mixing framework for endpoint criticality governed by one relevant scaling field together with a marginally irrelevant one, a setting that lies outside the conventional two-relevant-field formulation. By constructing a finite-size pseudocritical manifold, the framework removes the normal relevant detuning and exposes the residual marginal drift, enabling controlled histogram- and Binder-based finite-size analyses. We apply this approach to the frustrated square-lattice $J_1$--$J_2$ Ising model, where the location and even the nature of the stripe-ordering endpoint have remained controversial for decades. The endpoint is isolated directly as a distinct singular point, rather than inferred from where the phase boundary appears most Potts-like, and its asymptotic criticality is shown to follow four-state Potts universality with logarithmic corrections. This identification is independently supported by direct comparison with the Potts point of the Ashkin--Teller model and by consistent Binder scaling in both the magnetic and nematic sectors. Our results resolve a longstanding numerical ambiguity in a paradigmatic frustrated Ising system and establish a general framework for extracting asymptotic endpoint criticality in the presence of marginal flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25946 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized field mixing for endpoint criticality with marginal flow: resolving the four-state Potts endpoint in the square-lattice $J_1$--$J_2$ Ising model Sun, Yihua Fan, Yuchen Statistical Mechanics Strongly Correlated Electrons Identifying the asymptotic criticality of a critical endpoint is challenging, as pseudo-first-order signatures persist over accessible system sizes and mask its underlying critical nature. This ambiguity is amplified at endpoints controlled by a marginally irrelevant scaling field, where logarithmic flow delays the onset of asymptotic scaling. Here we develop a generalized field-mixing framework for endpoint criticality governed by one relevant scaling field together with a marginally irrelevant one, a setting that lies outside the conventional two-relevant-field formulation. By constructing a finite-size pseudocritical manifold, the framework removes the normal relevant detuning and exposes the residual marginal drift, enabling controlled histogram- and Binder-based finite-size analyses. We apply this approach to the frustrated square-lattice $J_1$--$J_2$ Ising model, where the location and even the nature of the stripe-ordering endpoint have remained controversial for decades. The endpoint is isolated directly as a distinct singular point, rather than inferred from where the phase boundary appears most Potts-like, and its asymptotic criticality is shown to follow four-state Potts universality with logarithmic corrections. This identification is independently supported by direct comparison with the Potts point of the Ashkin--Teller model and by consistent Binder scaling in both the magnetic and nematic sectors. Our results resolve a longstanding numerical ambiguity in a paradigmatic frustrated Ising system and establish a general framework for extracting asymptotic endpoint criticality in the presence of marginal flow. |
| title | Generalized field mixing for endpoint criticality with marginal flow: resolving the four-state Potts endpoint in the square-lattice $J_1$--$J_2$ Ising model |
| topic | Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.25946 |