Fixed Points and Universality Classes in Coupled Kardar-Parisi-Zhang Equations
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908389188042752 |
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| author | Roy, Dipankar Dhar, Abhishek Kulkarni, Manas Spohn, Herbert |
| author_facet | Roy, Dipankar Dhar, Abhishek Kulkarni, Manas Spohn, Herbert |
| contents | We study coupled KPZ equations with three control parameters $X,Y,T$. These equations are used in the context of stretched polymers in a random medium, for the spacetime spin-spin correlator of the isotropic quantum Heisenberg chain, and for exciton-polariton condensates. In an earlier article we investigated merely the diagonal $X=Y$, $T=1$. Then the stationary measure is delta-correlated Gaussian and the dynamical exponent is obtained numerically to be close to $z = \tfrac{3}{2}$. We observed that the scaling functions of the dynamic correlator change smoothly when varying $X$. In this contribution, the analysis is extended to the whole $X$-$Y$-$T$ plane. Solutions are stable only if $XY \geq 0$. Based on numerical simulations, the static correlator still has rapid decay. We argue that the parameter space is foliated into distinct universality classes. They are labeled by $X$ and consist of half-planes parallel to the $Y$-$T$ plane containing the point $(X,X,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed Points and Universality Classes in Coupled Kardar-Parisi-Zhang Equations Roy, Dipankar Dhar, Abhishek Kulkarni, Manas Spohn, Herbert Statistical Mechanics Mathematical Physics Probability We study coupled KPZ equations with three control parameters $X,Y,T$. These equations are used in the context of stretched polymers in a random medium, for the spacetime spin-spin correlator of the isotropic quantum Heisenberg chain, and for exciton-polariton condensates. In an earlier article we investigated merely the diagonal $X=Y$, $T=1$. Then the stationary measure is delta-correlated Gaussian and the dynamical exponent is obtained numerically to be close to $z = \tfrac{3}{2}$. We observed that the scaling functions of the dynamic correlator change smoothly when varying $X$. In this contribution, the analysis is extended to the whole $X$-$Y$-$T$ plane. Solutions are stable only if $XY \geq 0$. Based on numerical simulations, the static correlator still has rapid decay. We argue that the parameter space is foliated into distinct universality classes. They are labeled by $X$ and consist of half-planes parallel to the $Y$-$T$ plane containing the point $(X,X,1)$. |
| title | Fixed Points and Universality Classes in Coupled Kardar-Parisi-Zhang Equations |
| topic | Statistical Mechanics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2504.04162 |