Correlated Noise and Critical Dimensions (2302.13666v6)
Abstract: In equilibrium, the Mermin-Wagner theorem prohibits the continuous symmetry breaking for all dimensions $d\leq 2$. In this work, we discuss that this limitation can be circumvented in non-equilibrium systems driven by the spatio-temporally long-range anticorrelated noise. We first compute the lower and upper critical dimensions of the $O(n)$ model driven by the spatio-temporally correlated noise by means of the dimensional analysis. Next, we consider the spherical model, which corresponds to the large $n$ limit of the $O(n)$ model and allows us to compute the critical dimensions and critical exponents, analytically. Both results suggest that the critical dimensions increase when the noise is positively correlated in space and time, and decrease when anticorrelated. We also report that the spherical model with the correlated noise shows the hyperuniformity and giant number fluctuation even well above the critical point.
- H. Nishimori and G. Ortiz, Elements of phase transitions and critical phenomena (Oup Oxford, 2010).
- Y. Imry and S.-k. Ma, Phys. Rev. Lett. 35, 1399 (1975).
- W. Janke and R. Villanova, Physics Letters A 209, 179 (1995).
- H. Barghathi and T. Vojta, Phys. Rev. Lett. 113, 120602 (2014).
- J. Luck, Journal of Physics A: Mathematical and General 20, 1259 (1987).
- C. Sire, International Journal of Modern Physics B 7, 1551 (1993).
- N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).
- K. E. Bassler and Z. Rácz, Phys. Rev. E 52, R9 (1995).
- J. Toner and Y. Tu, Phys. Rev. Lett. 75, 4326 (1995).
- S. Torquato, Physics Reports 745, 1 (2018).
- B. Zhang and A. Snezhko, Phys. Rev. Lett. 128, 218002 (2022).
- D. Hexner and D. Levine, Physical review letters 118, 020601 (2017).
- Q.-L. Lei and R. Ni, Proceedings of the National Academy of Sciences 116, 22983 (2019).
- Y. Kuroda and K. Miyazaki, arXiv preprint arXiv:2305.06298 (2023).
- H. Ikeda and Y. Kuroda, arXiv preprint arXiv:2304.14235 (2023).
- J.-P. Bouchaud and A. Georges, Physics reports 195, 127 (1990).
- I. Eliazar and J. Klafter, Proceedings of the National Academy of Sciences 106, 12251 (2009).
- E. Katzav and M. Schwartz, Phys. Rev. E 70, 011601 (2004).
- D. Squizzato and L. Canet, Phys. Rev. E 100, 062143 (2019).
- J. Kim and S. Torquato, Phys. Rev. B 97, 054105 (2018).
- R. Zwanzig, Nonequilibrium statistical mechanics (Oxford university press, 2001).
- T. Nattermann, in Spin glasses and random fields (World Scientific, 1998) pp. 277–298.
- M. Henkel and M. Pleimling, “Non-equilibrium phase transitions vol. 2: ageing and dynamical scaling far from equilibrium,” (2010).
- T. H. Berlin and M. Kac, Physical Review 86, 821 (1952).
- M. Kac and C. J. Thompson, Journal of Mathematical Physics 18, 1650 (1977).
- A. Onuki, Phase transition dynamics (Cambridge University Press, 2002).
- F. Höfling and T. Franosch, Reports on Progress in Physics 76, 046602 (2013).
- J. García-Ojalvo and J. M. Sancho, Phys. Rev. E 49, 2769 (1994).
- R. F. Voss and J. Clarke, Phys. Rev. B 13, 556 (1976).
- P. Dutta and P. M. Horn, Rev. Mod. Phys. 53, 497 (1981).
- E. Milotti, arXiv preprint physics/0204033 (2002).
- Y. Zhang and É. Fodor, arXiv preprint arXiv:2208.06831 (2022).
- B. Liebchen and D. Levis, Europhysics Letters 139, 67001 (2022).
Sponsor
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.