In this paper, we establish a general theta function identity. It is a common origin of many theta function identities. From which many classical and new modular equations are derived. All the proofs are elementary.
A one step real space renormalization group(RSRG)transformation is used to study the ferromagnetic(FM)Potts model on the two dimemsional (2D) octagonal quasi periodic tiling(OQT). The critical exponents of the ...A one step real space renormalization group(RSRG)transformation is used to study the ferromagnetic(FM)Potts model on the two dimemsional (2D) octagonal quasi periodic tiling(OQT). The critical exponents of the correlation length in the q =1,2,3,4 cases and the crtitical surface of the Ising model are obtained. The results are discussed by comparing with previous results on the OQT and the square lattice(SQL).展开更多
基金Supported by the National Natural Science Foundation of China（11071107, 11371184）
文摘In this paper, we establish a general theta function identity. It is a common origin of many theta function identities. From which many classical and new modular equations are derived. All the proofs are elementary.
文摘A one step real space renormalization group(RSRG)transformation is used to study the ferromagnetic(FM)Potts model on the two dimemsional (2D) octagonal quasi periodic tiling(OQT). The critical exponents of the correlation length in the q =1,2,3,4 cases and the crtitical surface of the Ising model are obtained. The results are discussed by comparing with previous results on the OQT and the square lattice(SQL).
