Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.21803 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915816519237632 |
|---|---|
| author | Satynska, Yelyzaveta Robb, Daniel T. |
| author_facet | Satynska, Yelyzaveta Robb, Daniel T. |
| contents | Dynamic phase transitions of periodically forced mean-field ferromagnets are often described by a single order parameter and a scalar conjugate field. Building from previous work, we show that, at the critical period $P_c$ of the mean-field Ginzburg-Landau (MFGL) dynamics with energy $F(m)=am^2+bm^4-hm$, the correct conjugate field is the entire even-Fourier component part of the applied field. The correct order parameter is $z_k=\sqrt{\bigl|\,m_k^2-|m_{k,c}|^2\,\bigr|}$, where $m_k$ is the $k^{th}$ Fourier component of the magnetization m(t), and $m_{k,c}$ is the $k^{th}$ Fourier component at the critical period. Using high-accuracy limit-cycle integration and Fourier analysis, we first confirm that, for periodic fields that contain only odd components, the symmetry-broken branch below $P_c$ exhibits $z_k \propto \varepsilon^{1/2}$ (computationally tested for modes $k\le30$), where $\varepsilon=(P_c-P)/P_c$. This provides strong evidence that the 1/2 scaling holds for all Fourier modes. We then find three robust facts: (1) Exactly at $P_c$, adding a small perturbation composed of even Fourier components with an overall field multiplier $h_{mult}$ yields $z_k \propto h_{mult}^{1/3}$ across many $k$. (2) Mode-resolved deviations obey a parity rule: $|δm_{2n}| \propto h_{mult}^{1/3}$ and $|δm_{2n+1}| \propto h_{mult}^{2/3}$. (3) These scalings persist in two MFGL models with higher-order nonlinearities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamic Phase Transitions in Mean-Field Ginzburg-Landau Models: Conjugate Fields and Fourier-Mode Scaling Satynska, Yelyzaveta Robb, Daniel T. Statistical Mechanics Computational Physics Dynamic phase transitions of periodically forced mean-field ferromagnets are often described by a single order parameter and a scalar conjugate field. Building from previous work, we show that, at the critical period $P_c$ of the mean-field Ginzburg-Landau (MFGL) dynamics with energy $F(m)=am^2+bm^4-hm$, the correct conjugate field is the entire even-Fourier component part of the applied field. The correct order parameter is $z_k=\sqrt{\bigl|\,m_k^2-|m_{k,c}|^2\,\bigr|}$, where $m_k$ is the $k^{th}$ Fourier component of the magnetization m(t), and $m_{k,c}$ is the $k^{th}$ Fourier component at the critical period. Using high-accuracy limit-cycle integration and Fourier analysis, we first confirm that, for periodic fields that contain only odd components, the symmetry-broken branch below $P_c$ exhibits $z_k \propto \varepsilon^{1/2}$ (computationally tested for modes $k\le30$), where $\varepsilon=(P_c-P)/P_c$. This provides strong evidence that the 1/2 scaling holds for all Fourier modes. We then find three robust facts: (1) Exactly at $P_c$, adding a small perturbation composed of even Fourier components with an overall field multiplier $h_{mult}$ yields $z_k \propto h_{mult}^{1/3}$ across many $k$. (2) Mode-resolved deviations obey a parity rule: $|δm_{2n}| \propto h_{mult}^{1/3}$ and $|δm_{2n+1}| \propto h_{mult}^{2/3}$. (3) These scalings persist in two MFGL models with higher-order nonlinearities. |
| title | Dynamic Phase Transitions in Mean-Field Ginzburg-Landau Models: Conjugate Fields and Fourier-Mode Scaling |
| topic | Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2510.21803 |