Renormalization Group Theory of Eigen Microstates

Teng Liu, Gao Ke Hu, Jia Qi Dong, Jing Fang Fan, Mao Xin Liu, Xiao Song Chen

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 σ 1 has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relation σ1b=bβ/νσ1, where β and ν 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.

Original languageEnglish
Article number080503
JournalChinese Physics Letters
Issue number8
StatePublished - 1 Jul 2022
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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