Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions
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| Format: | Preprint |
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2025
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| author | Kuttanikkad, Vishnu Pulloor Prakash, Abhishodh Narayanan, Rajesh Chanda, Titas |
| author_facet | Kuttanikkad, Vishnu Pulloor Prakash, Abhishodh Narayanan, Rajesh Chanda, Titas |
| contents | We present a comprehensive study on the frustrated $J_1$-$J_2$ classical $q$-state clock model with even $q>4$ on a two-dimensional square lattice, revealing a rich ensemble of phases driven by competing interactions. In the unfrustrated regime ($J_1>2J_2$), the model reproduces the standard clock model phenomenology: a low-temperature $\mathbb{Z}_q$-broken ferromagnet, an intermediate XY-like critical quasi-long-range-ordered (QLRO) phase with emergent $U(1)$ symmetry, and a high-temperature paramagnet. For $J_1<2J_2$, frustration stabilizes five distinct regimes: the disordered paramagnet, a stripe-ordered phase breaking $\mathbb{Z}_q\times\mathbb{Z}_2$ symmetry, two $\mathbb{Z}_2$-broken nematic phases (one with and one without QLRO), and an exotic stripe phase with emergent discrete $\mathbb{Z}_q$ spin degrees of freedom prohibited in the microscopic Hamiltonian. Remarkably, this seemingly forbidden $\mathbb{Z}_q$ order emerges via a relevant operator in the infrared long-wavelength limit, rather than from an irrelevant perturbation, highlighting a non-standard route to emergence. Using large-scale corner transfer matrix renormalization group calculations, complemented by classical Monte Carlo simulations, we map the complete phase diagram and identify Berezinskii-Kosterlitz-Thouless, Ising, first-order, and unconventional Landau-incompatible transitions between different phases. Finally, we propose an effective field-theoretic framework that encompasses these emergent orders and their interwoven transitions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_05194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions Kuttanikkad, Vishnu Pulloor Prakash, Abhishodh Narayanan, Rajesh Chanda, Titas Statistical Mechanics Strongly Correlated Electrons We present a comprehensive study on the frustrated $J_1$-$J_2$ classical $q$-state clock model with even $q>4$ on a two-dimensional square lattice, revealing a rich ensemble of phases driven by competing interactions. In the unfrustrated regime ($J_1>2J_2$), the model reproduces the standard clock model phenomenology: a low-temperature $\mathbb{Z}_q$-broken ferromagnet, an intermediate XY-like critical quasi-long-range-ordered (QLRO) phase with emergent $U(1)$ symmetry, and a high-temperature paramagnet. For $J_1<2J_2$, frustration stabilizes five distinct regimes: the disordered paramagnet, a stripe-ordered phase breaking $\mathbb{Z}_q\times\mathbb{Z}_2$ symmetry, two $\mathbb{Z}_2$-broken nematic phases (one with and one without QLRO), and an exotic stripe phase with emergent discrete $\mathbb{Z}_q$ spin degrees of freedom prohibited in the microscopic Hamiltonian. Remarkably, this seemingly forbidden $\mathbb{Z}_q$ order emerges via a relevant operator in the infrared long-wavelength limit, rather than from an irrelevant perturbation, highlighting a non-standard route to emergence. Using large-scale corner transfer matrix renormalization group calculations, complemented by classical Monte Carlo simulations, we map the complete phase diagram and identify Berezinskii-Kosterlitz-Thouless, Ising, first-order, and unconventional Landau-incompatible transitions between different phases. Finally, we propose an effective field-theoretic framework that encompasses these emergent orders and their interwoven transitions. |
| title | Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions |
| topic | Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2505.05194 |