Universal exotic dynamics in critical mesoscopic systems: Simulating the square root of Avogadro's number of spins
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908519457882112 |
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| author | Bisson, Mauro Vasilopoulos, Alexandros Bernaschi, Massimo Fatica, Massimiliano Fytas, Nikolaos G. Pemartín, Isidoro González-Adalid Martín-Mayor, Víctor |
| author_facet | Bisson, Mauro Vasilopoulos, Alexandros Bernaschi, Massimo Fatica, Massimiliano Fytas, Nikolaos G. Pemartín, Isidoro González-Adalid Martín-Mayor, Víctor |
| contents | We explicitly demonstrate the universality of critical dynamics through unprecedented large-scale GPU-based simulations of two out-of-equilibrium processes, comparing the behavior of spin-$1/2$ Ising and spin-$1$ Blume-Capel models on a square lattice. In the first protocol, a completely disordered system is instantaneously brought into contact with a thermal bath at the critical temperature, allowing it to evolve until the coherence length exceeds $10^{3}$ lattice spacings. Finite-size effects are negligible due to the mesoscopic scale of the lattice sizes studied, with linear dimensions up to $L=2^{22}$ and $2^{19}$ for the Ising and Blume-Capel models, respectively. Our numerical data, and the subsequent analysis, demonstrate a strong dynamic universality between the two models and provide the most precise estimate to date of the dynamic critical exponent for this universality class, $z = 2.1676(1)$. In the second protocol, we corroborate the role of the universal ratio of dynamic and static length scales in achieving an exponential acceleration in the approach to equilibrium just \emph{above} the critical temperature, through a time-dependent variation of the thermal bath temperature. The results presented in this work leverage our CUDA-based numerical code, breaking the world record for the simulation speed of the Ising model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal exotic dynamics in critical mesoscopic systems: Simulating the square root of Avogadro's number of spins Bisson, Mauro Vasilopoulos, Alexandros Bernaschi, Massimo Fatica, Massimiliano Fytas, Nikolaos G. Pemartín, Isidoro González-Adalid Martín-Mayor, Víctor Statistical Mechanics Computational Physics We explicitly demonstrate the universality of critical dynamics through unprecedented large-scale GPU-based simulations of two out-of-equilibrium processes, comparing the behavior of spin-$1/2$ Ising and spin-$1$ Blume-Capel models on a square lattice. In the first protocol, a completely disordered system is instantaneously brought into contact with a thermal bath at the critical temperature, allowing it to evolve until the coherence length exceeds $10^{3}$ lattice spacings. Finite-size effects are negligible due to the mesoscopic scale of the lattice sizes studied, with linear dimensions up to $L=2^{22}$ and $2^{19}$ for the Ising and Blume-Capel models, respectively. Our numerical data, and the subsequent analysis, demonstrate a strong dynamic universality between the two models and provide the most precise estimate to date of the dynamic critical exponent for this universality class, $z = 2.1676(1)$. In the second protocol, we corroborate the role of the universal ratio of dynamic and static length scales in achieving an exponential acceleration in the approach to equilibrium just \emph{above} the critical temperature, through a time-dependent variation of the thermal bath temperature. The results presented in this work leverage our CUDA-based numerical code, breaking the world record for the simulation speed of the Ising model. |
| title | Universal exotic dynamics in critical mesoscopic systems: Simulating the square root of Avogadro's number of spins |
| topic | Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2503.14688 |