摘要
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 eigenvalueσ1 has two trivial fixed points at low and high temperature limits and a critical fixed point with the RG relationσb1=bβ/νσ1,whereβandνare 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.
作者
刘腾
胡高科
董家奇
樊京芳
刘卯鑫
陈晓松
Teng Liu;Gao-Ke Hu;Jia-Qi Dong;Jing-Fang Fan;Mao-Xin Liu;and Xiao-Song Chen(School of Systems Science/Institute of Nonequilibrium Systems,Beijing Normal University,Beijing 100875,China;Lanzhou 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;School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)
基金
supported by the National Natural Science Foundation of China(Grant No.12135003)。