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
用Yukawa势能函数表达胶体颗粒之间的吸引作用 .用Duh Mier Y Teran状态方程表达液相Helmholtz自由能 .用一阶微扰理论、固体硬球径向分布函数解析式和改进的胞腔模型建立固相状态方程 .结合建立的状态方程和重整化群(RenormalizationGr...用Yukawa势能函数表达胶体颗粒之间的吸引作用 .用Duh Mier Y Teran状态方程表达液相Helmholtz自由能 .用一阶微扰理论、固体硬球径向分布函数解析式和改进的胞腔模型建立固相状态方程 .结合建立的状态方程和重整化群(RenormalizationGroup ,RG)理论 ,研究了胶体模型体系的液 -液相平衡和液 -固相平衡 .研究表明 ,颗粒之间色散作用量程参数的变化对胶体模型体系的相行为有重要影响 .展开更多
An equation of state （EOS） applicable for both the uniform and non-uniform fluids was established by using the density-gradient expansion, in which the influence parameter x[ρ（r）,T] was obtained by the use of dir...An equation of state （EOS） applicable for both the uniform and non-uniform fluids was established by using the density-gradient expansion, in which the influence parameter x[ρ（r）,T] was obtained by the use of direct correlation function. The density functional theory （DFT） provides a framework under which both the phase equilibria and interfacial properties can be investigated within a single set of molecular parameters. The phase equilibria inside the critical region can be improved by the renormalization group theory （RGT）. However, the correction of interfacial properties by DFT and RGT is computationally difficult. In the present work, the density gradient theory （DGT） in which κ[ρ（r）,T] is treated as a constant is used to combine with the RGT for interfacial properties inside the critical region.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
The unitary correlation operator method （UCOM） and the similarity renormalization group theory （SRG） are compared and discussed in the framework of the no-core Monte Carlo shell model （MCSM） calculations for ^3H...The unitary correlation operator method （UCOM） and the similarity renormalization group theory （SRG） are compared and discussed in the framework of the no-core Monte Carlo shell model （MCSM） calculations for ^3H and ^4He. The treatment of spurious center-of-mass motion by Lawson＇s prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson＇s prescription parameter βc.m. values. The UCOM potentials obtain faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations （NCSM）. These differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of the potentials of SRG and UCOM.展开更多
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Project Supported by the National Naturai Science Foundation of＇C-hina （No. 20576030） and the Key Program Foundation from the North China Electric Power University.
文摘An equation of state （EOS） applicable for both the uniform and non-uniform fluids was established by using the density-gradient expansion, in which the influence parameter x[ρ（r）,T] was obtained by the use of direct correlation function. The density functional theory （DFT） provides a framework under which both the phase equilibria and interfacial properties can be investigated within a single set of molecular parameters. The phase equilibria inside the critical region can be improved by the renormalization group theory （RGT）. However, the correction of interfacial properties by DFT and RGT is computationally difficult. In the present work, the density gradient theory （DGT） in which κ[ρ（r）,T] is treated as a constant is used to combine with the RGT for interfacial properties inside the critical region.
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.
基金Supported by Fundamental Research Funds for the Central Universities(JUSRP1035)National Natural Science Foundation of China(11305077)
文摘The unitary correlation operator method （UCOM） and the similarity renormalization group theory （SRG） are compared and discussed in the framework of the no-core Monte Carlo shell model （MCSM） calculations for ^3H and ^4He. The treatment of spurious center-of-mass motion by Lawson＇s prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson＇s prescription parameter βc.m. values. The UCOM potentials obtain faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations （NCSM）. These differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of the potentials of SRG and UCOM.
