Monte Carlo study of the $O(2)$-invariant $ϕ^4$ theory with a cubic perturbation in three dimensions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909863777402880 |
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| author | Hasenbusch, Martin |
| author_facet | Hasenbusch, Martin |
| contents | We study the $2$-component $ϕ^4$ model on the simple cubic lattice in the presence of a cubic, or equivalently, a $\mathbb{D}_4$ invariant perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finite size scaling analysis of the data. We follow previous work on the $3$-component case. We study the RG flow from the decoupled Ising fixed point into the $O(2)$-invariant one and towards the fluctuation induced first order transition. To this end we study the behavior of phenomenological couplings. At the $O(2)$-invariant fixed point we obtain the estimate $Y_4=-0.1118(10)$ of the RG-exponent of the perturbation. Note that the small modulus of $Y_4$ means that the RG flow is slow. Hence, in order to interpret experiments or Monte Carlo simulations of lattice models, which are effectively described by the $ϕ^4$ model with a cubic term, we have to consider the RG flow beyond the neighborhood of the fixed points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monte Carlo study of the $O(2)$-invariant $ϕ^4$ theory with a cubic perturbation in three dimensions Hasenbusch, Martin Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory We study the $2$-component $ϕ^4$ model on the simple cubic lattice in the presence of a cubic, or equivalently, a $\mathbb{D}_4$ invariant perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finite size scaling analysis of the data. We follow previous work on the $3$-component case. We study the RG flow from the decoupled Ising fixed point into the $O(2)$-invariant one and towards the fluctuation induced first order transition. To this end we study the behavior of phenomenological couplings. At the $O(2)$-invariant fixed point we obtain the estimate $Y_4=-0.1118(10)$ of the RG-exponent of the perturbation. Note that the small modulus of $Y_4$ means that the RG flow is slow. Hence, in order to interpret experiments or Monte Carlo simulations of lattice models, which are effectively described by the $ϕ^4$ model with a cubic term, we have to consider the RG flow beyond the neighborhood of the fixed points. |
| title | Monte Carlo study of the $O(2)$-invariant $ϕ^4$ theory with a cubic perturbation in three dimensions |
| topic | Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.19473 |