| GENERAL |
|
|
|
|
Renormalization Group Theory of Eigen Microstates |
| Teng Liu1†, Gao-Ke Hu1†, Jia-Qi Dong2, Jing-Fang Fan1, Mao-Xin Liu3, and Xiao-Song Chen1* |
1School of Systems Science/Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100875, China
2Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China
3School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
|
|
| Cite this article: |
|
Teng Liu, Gao-Ke Hu, Jia-Qi Dong et al 2022 Chin. Phys. Lett. 39 080503 |
|
|
|
|
Abstract We propose a renormalization group (RG) theory of eigen microstates, which are introduced in the statistical ensemble composed of microstates obtained from experiments or computer simulations. A microstate in the ensemble can be considered as a linear superposition of eigen microstates with probability amplitudes equal to their eigenvalues. Under the renormalization of a factor $b$, the largest eigenvalue $\sigma_1$ has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relation $\sigma_1^b = b^{\beta/\nu} \sigma_1$, where $\beta$ and $\nu$ are the critical exponents of order parameter and correlation length, respectively. With the Ising model in different dimensions, it has been demonstrated that the RG theory of eigen microstates is able to identify the critical point and to predict critical exponents and the universality class. Our theory can be used in research of critical phenomena both in equilibrium and non-equilibrium systems without considering the Hamiltonian, which is the foundation of Wilson's RG theory and is absent for most complex systems.
|
|
Received: 07 June 2022
Express Letter
Published: 19 July 2022
|
|
|
|
|
|
|
|
| [1] | Anderson P W 1972 Science 177 393 |
| [2] | Stanley H E 1987 Introduction to Phase Transition and Critical Phenomena (New York: Oxford University Press) |
| [3] | Landau L D 1937 Phys. Z. Sowjetunion 11 26 |
| [4] | Kadanoff L P 1966 Phys. Phys. Fiz. 2 263 |
| [5] | Wilson K G 1971 Phys. Rev. 4 3174 |
| [6] | Wilson K G 1971 Phys. Rev. 4 3184 |
| [7] | Wilson K G and Fisher M E 1972 Phys. Rev. Lett. 28 240 |
| [8] | Wilson K G and Kogut J 1974 Phys. Rep. 12 75 |
| [9] | Barmatz M, Hahn I, Lipa J A and Duncan R V 2007 Rev. Mod. Phys. 79 1 |
| [10] | Kadanoff L P 1971 Critical Phenomena, in Proceedings of the Enrico Fermi International School of Physics, Course LI, edited by Green M S (New York: Academic) p 100 |
| [11] | Stauffer D, Ferer M and Wortis M 1972 Phys. Rev. Lett. 29 345 |
| [12] | Aharony A 1974 Phys. Rev. B 9 2107 |
| [13] | Geber P R 1975 J. Phys. A 8 67 |
| [14] | Hohenberg P C, Aharony A, Halperin B J and Siggia E D 1976 Phys. Rev. B 13 2986 |
| [15] | Wegner F 1976 in Phase Transitions and Critical Phenomena, edited by Domb C and Green M S (New York: Academic) p 7 |
| [16] | Chen X S and Dohm V 2004 Phys. Rev. E 70 056136 |
| [17] | Chen X S 2020 Chin. Phys. Lett. 37 080103 |
| [18] | Selke W and Shchur L N 2005 J. Phys. A 38 L739 |
| [19] | Schulte M and Drope C 2005 Int. J. Mod. Phys. 16 1217 |
| [20] | Muñoz M A 2018 Rev. Mod. Phys. 90 031001 |
| [21] | Dorogovtsev S N, Goltsev A V and Mendes J F F 2008 Rev. Mod. Phys. 80 1275 |
| [22] | Hu G K, Liu T, Liu M X, Chen W and Chen X S 2019 Sci. Chin. Phys. Mech. & Astron. 62 990511 |
| [23] | Sun Y, Hu G K, Zhang Y W, Lu B, Lu Z H, Fan J F, Li X T, Deng Q M and Chen X S 2021 Commun. Theor. Phys. 73 065603 |
| [24] | Li X, Xue T T, Sun Y, Fan J F, Li H, Liu M X, Z G, Di Z R and Chen X S 2021 Chin. Phys. B 30 128703 |
| [25] | Chen X J, Ying N, Chen D, Zhang Y W, Lu B, Fan J F and Chen X S 2021 Chaos 31 071102 |
| [26] | Campostrini M, Pelissetto A, Rossi P and Vicari E 2002 Phys. Rev. E 65 066127 |
| [27] | Yang Z Q, Liu M X and Chen X S 2017 Sci. Chin. Phys. Mech. & Astron. 60 020521 |
| [28] | Privman V and Fisher M E 1984 Phys. Rev. B 30 322 |
| [29] | Gibbs J W 1902 Elementary Principles in Statistical Mechanics (New York: Charles Scribner's Sons) |
| [30] | Li X T and Chen X S 2016 Commun. Theor. Phys. 66 355 |
| [31] | Bradde S and Bialek W 2017 J. Stat. Phys. 167 462 |
| [32] | Wolff U 1989 Phys. Rev. Lett. 62 361 |
| [33] | Ferrenberg A M, Xu J H and Landau D P 2018 Phys. Rev. E 97 043301 |
| [34] | Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic) |
| [35] | Chen X S and Dohm V 2000 Eur. Phys. J. B 15 283 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
