Dynamical phase transitions in $XY$ model: a Monte Carlo and mean-field theory study
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| Format: | Preprint |
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2024
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| _version_ | 1866915014533709824 |
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| author | Pal, Mainak Baez, William D. Majumdar, Pushan Sen, Arnab Datta, Trinanjan |
| author_facet | Pal, Mainak Baez, William D. Majumdar, Pushan Sen, Arnab Datta, Trinanjan |
| contents | We investigate the dynamical phases and phase transitions arising in a classical two-dimensional anisotropic $XY$ model under the influence of a periodically driven temporal external magnetic field in the form of a symmetric square wave. We use a combination of finite temperature classical Monte Carlo simulation, implemented within a CPU + GPU paradigm, utilizing local dynamics provided by the Glauber algorithm and a phenomenological equation-of-motion approach based on relaxational dynamics governed by the time-dependent free energy within a mean-field approximation to study the model. We investigate several parameter regimes of the variables (magnetic field, anisotropy, and the external drive frequency) that influence the anisotropic $XY$ system. We identify four possible dynamical phases -- Ising-SBO, Ising-SRO, $XY$-SBO and $XY$-SRO. Both techniques indicate that only three of them (Ising-SRO, Ising-SBO, and $XY$-SRO) are stable dynamical phases in the thermodynamic sense. Within the Monte Carlo framework, a finite size scaling analysis shows that $XY$-SBO does not survive in the thermodynamic limit giving way to either an Ising-SBO or a $XY$-SRO regime. The finite size scaling analysis further shows that the transitions between the three remaining dynamical phases either belong to the two-dimensional Ising universality class or are first-order in nature. The mean-field calculations yield three stable dynamical phases, i.e., Ising-SRO, Ising-SBO and $XY$-SRO, where the final steady state is independent of the initial condition chosen to evolve the equations of motion, as well as a region of bistability where the system either flows to Ising-SBO or $XY$-SRO (Ising-SRO) depending on the initial condition. Unlike the stable dynamical phases, the $XY$-SBO represents a transient feature that is eventually lost to either Ising-SBO or $XY$-SRO. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_07505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical phase transitions in $XY$ model: a Monte Carlo and mean-field theory study Pal, Mainak Baez, William D. Majumdar, Pushan Sen, Arnab Datta, Trinanjan Statistical Mechanics We investigate the dynamical phases and phase transitions arising in a classical two-dimensional anisotropic $XY$ model under the influence of a periodically driven temporal external magnetic field in the form of a symmetric square wave. We use a combination of finite temperature classical Monte Carlo simulation, implemented within a CPU + GPU paradigm, utilizing local dynamics provided by the Glauber algorithm and a phenomenological equation-of-motion approach based on relaxational dynamics governed by the time-dependent free energy within a mean-field approximation to study the model. We investigate several parameter regimes of the variables (magnetic field, anisotropy, and the external drive frequency) that influence the anisotropic $XY$ system. We identify four possible dynamical phases -- Ising-SBO, Ising-SRO, $XY$-SBO and $XY$-SRO. Both techniques indicate that only three of them (Ising-SRO, Ising-SBO, and $XY$-SRO) are stable dynamical phases in the thermodynamic sense. Within the Monte Carlo framework, a finite size scaling analysis shows that $XY$-SBO does not survive in the thermodynamic limit giving way to either an Ising-SBO or a $XY$-SRO regime. The finite size scaling analysis further shows that the transitions between the three remaining dynamical phases either belong to the two-dimensional Ising universality class or are first-order in nature. The mean-field calculations yield three stable dynamical phases, i.e., Ising-SRO, Ising-SBO and $XY$-SRO, where the final steady state is independent of the initial condition chosen to evolve the equations of motion, as well as a region of bistability where the system either flows to Ising-SBO or $XY$-SRO (Ising-SRO) depending on the initial condition. Unlike the stable dynamical phases, the $XY$-SBO represents a transient feature that is eventually lost to either Ising-SBO or $XY$-SRO. |
| title | Dynamical phase transitions in $XY$ model: a Monte Carlo and mean-field theory study |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2402.07505 |