Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs
Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and majority voter models. When these nonequilibrium...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-12-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/25/12/1615 |
| _version_ | 1797381224240513024 |
|---|---|
| author | Adam Lipowski António L. Ferreira Dorota Lipowska |
| author_facet | Adam Lipowski António L. Ferreira Dorota Lipowska |
| author_sort | Adam Lipowski |
| collection | DOAJ |
| description | Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and majority voter models. When these nonequilibrium models are driven by the heat-bath dynamics, their stationary characteristics, such as magnetization, are correctly reproduced by MFA as confirmed by Monte Carlo simulations. It turns out that MFA reproduces the same result as the generating functional analysis that is expected to provide the exact description of such models. We argue that on directed regular random graphs, the neighbors of a given vertex are typically uncorrelated, and that is why MFA for models with heat-bath dynamics provides their exact description. For models with Metropolis dynamics, certain additional correlations become relevant, and MFA, which neglects these correlations, is less accurate. Models with heat-bath dynamics undergo continuous phase transition, and at the critical point, the power-law time decay of the order parameter exhibits the behavior of the Ising mean-field universality class. Analogous phase transitions for models with Metropolis dynamics are discontinuous. |
| first_indexed | 2024-03-08T20:48:18Z |
| format | Article |
| id | doaj.art-f82e94828d7c421cbe727a98afb82a94 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-08T20:48:18Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f82e94828d7c421cbe727a98afb82a942023-12-22T14:07:22ZengMDPI AGEntropy1099-43002023-12-012512161510.3390/e25121615Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random GraphsAdam Lipowski0António L. Ferreira1Dorota Lipowska2Faculty of Physics, Adam Mickiewicz University in Poznań, 61-614 Poznań, PolandDepartamento de Física, I3N, Universidade de Aveiro, 3810-193 Aveiro, PortugalFaculty of Modern Languages and Literatures, Adam Mickiewicz University in Poznań, 61-874 Poznań, PolandUsing a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and majority voter models. When these nonequilibrium models are driven by the heat-bath dynamics, their stationary characteristics, such as magnetization, are correctly reproduced by MFA as confirmed by Monte Carlo simulations. It turns out that MFA reproduces the same result as the generating functional analysis that is expected to provide the exact description of such models. We argue that on directed regular random graphs, the neighbors of a given vertex are typically uncorrelated, and that is why MFA for models with heat-bath dynamics provides their exact description. For models with Metropolis dynamics, certain additional correlations become relevant, and MFA, which neglects these correlations, is less accurate. Models with heat-bath dynamics undergo continuous phase transition, and at the critical point, the power-law time decay of the order parameter exhibits the behavior of the Ising mean-field universality class. Analogous phase transitions for models with Metropolis dynamics are discontinuous.https://www.mdpi.com/1099-4300/25/12/1615Ising modeldirected random graphsmean-field approximationnonequilibrium systems |
| spellingShingle | Adam Lipowski António L. Ferreira Dorota Lipowska Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs Entropy Ising model directed random graphs mean-field approximation nonequilibrium systems |
| title | Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs |
| title_full | Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs |
| title_fullStr | Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs |
| title_full_unstemmed | Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs |
| title_short | Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs |
| title_sort | heat bath and metropolis dynamics in ising like models on directed regular random graphs |
| topic | Ising model directed random graphs mean-field approximation nonequilibrium systems |
| url | https://www.mdpi.com/1099-4300/25/12/1615 |
| work_keys_str_mv | AT adamlipowski heatbathandmetropolisdynamicsinisinglikemodelsondirectedregularrandomgraphs AT antoniolferreira heatbathandmetropolisdynamicsinisinglikemodelsondirectedregularrandomgraphs AT dorotalipowska heatbathandmetropolisdynamicsinisinglikemodelsondirectedregularrandomgraphs |