In this paper we have completely determined:(1)all almost simple groups which act 2-transitively on one of their sets of Sylow p-subgroups.(2)all non-abelian simple groups T whose automorphism group acts 2-transitivel...In this paper we have completely determined:(1)all almost simple groups which act 2-transitively on one of their sets of Sylow p-subgroups.(2)all non-abelian simple groups T whose automorphism group acts 2-transitively on one of the sets of Sylow p-subgroups of T.(3)all finite groups which are 2-transitive on all their sets of Sylow subgroups.展开更多
We use the full-density matrix numerical renormalization group method to calculate the equilibrium dynamical correlation function C(ω) of the spin operator σ_(z) at finite temperature for the sub-ohmic spin-boson mo...We use the full-density matrix numerical renormalization group method to calculate the equilibrium dynamical correlation function C(ω) of the spin operator σ_(z) at finite temperature for the sub-ohmic spin-boson model.A peak is observed at the frequency ω_(T)~T in the curve of C(ω).The curve merges with the zero-temperature C(ω) in ω>>ω_(T) and deviates significantly from the zero-temperature curve in ω<<ω_(T).展开更多
Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability f...Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability fixed points of the theory, together with their associated instability exponents, are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar Ca model, below its critical temperature and near the instability points. Finite- time scaling and leading corrections to the scaling are considered. We also show that the instability exponents of the first-order phase transitions are equivalent to those of the Yang-Lee edge singularity, and employ the latter to improve our estimates of the former. The outcomes agree well with existing numerical results.展开更多
We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-c...We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found： a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two- loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as φ3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.展开更多
基金The first author acknowledges the support of OPR Scholarship of Australia The second author is supported by the National Natural Science Foundation of China.Thanks are also due to the Department of Mathematics,the University of Western Australia,where he
文摘In this paper we have completely determined:(1)all almost simple groups which act 2-transitively on one of their sets of Sylow p-subgroups.(2)all non-abelian simple groups T whose automorphism group acts 2-transitively on one of the sets of Sylow p-subgroups of T.(3)all finite groups which are 2-transitive on all their sets of Sylow subgroups.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11374362 and 11974420)the Fundamental Research Funds for the Central Universities,Chinathe Research Funds of Renmin University of China(Grant No.15XNLQ03)。
文摘We use the full-density matrix numerical renormalization group method to calculate the equilibrium dynamical correlation function C(ω) of the spin operator σ_(z) at finite temperature for the sub-ohmic spin-boson model.A peak is observed at the frequency ω_(T)~T in the curve of C(ω).The curve merges with the zero-temperature C(ω) in ω>>ω_(T) and deviates significantly from the zero-temperature curve in ω<<ω_(T).
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 10625420）.
文摘Through a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a φ^3 theory, we show that the instability fixed points of the theory, together with their associated instability exponents, are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar Ca model, below its critical temperature and near the instability points. Finite- time scaling and leading corrections to the scaling are considered. We also show that the instability exponents of the first-order phase transitions are equivalent to those of the Yang-Lee edge singularity, and employ the latter to improve our estimates of the former. The outcomes agree well with existing numerical results.
基金We thank Shuai Yin and Baoquan Feng for their helpful discussions. This work was supported by the National Natural Science foundation of PRC （Grants Nos. 10625420 and 11575297） and FRFCUC.
文摘We study the scaling and universal behavior of temperature-driven first-order phase transitions in scalar models. These transitions are found to exhibit rich phenomena, though they are controlled by a single complex-conjugate pair of imaginary fixed points of φ3 theory. Scaling theories and renormalization group theories are developed to account for the phenomena, and three universality classes with their own hysteresis exponents are found： a field-like thermal class, a partly thermal class, and a purely thermal class, designated, respectively, as Thermal Classes I, II, and III. The first two classes arise from the opposite limits of the scaling forms proposed and may cross over to each other depending on the temperature sweep rate. They are both described by a massless model and a purely massive model, both of which are equivalent and are derived from φ3 theory via symmetry. Thermal Class III characterizes the cooling transitions in the absence of applied external fields and is described by purely thermal models, which include cases in which the order parameters possess different symmetries and thus exhibit different universality classes. For the purely thermal models whose free energies contain odd-symmetry terms, Thermal Class III emerges only at the mean-field level and is identical to Thermal Class II. Fluctuations change the model into the other two models. Using the extant three- and two- loop results for the static and dynamic exponents for the Yang-Lee edge singularity, respectively, which falls into the same universality class as φ3 theory, we estimate the thermal hysteresis exponents of the various classes to the same precision. Comparisons with numerical results and experiments are briefly discussed.
