A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe t...A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe twoflavor normal quark matter. Depending on whether mo/A, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus mo is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value ofmo/A from QCD phenomenology, the phase transition must be of the first order.展开更多
As an example of the La-Mg-Y system, the method how to set up the themaodynamic model of individual phases was introduced in the process of thermodynamic optimization. The solution phases （liquid, body-centered cubic...As an example of the La-Mg-Y system, the method how to set up the themaodynamic model of individual phases was introduced in the process of thermodynamic optimization. The solution phases （liquid, body-centered cubic, face-centered cubic, hexagonal close-packed and double hexagonal close-packed） were modeled with the Redlich-Kister equation. The compound energy model has been used to describe the thermodynamic functions of the intermetallic compounds in the La-Mg-Y systems. The compounds Mg2Y, Mg24Y5, Mg12La, Mg17La2, Mg41Las, Mg3La and Mg2La in the La-Mg-Y system were treated as the formulae （Mg,Y）2（La,Mg,Y）, Mg24（La,Mg,Y）4Y, Mg12（La, Y）, Mg17（La,Y）2, Mg41（La,Y）5, Mg3（La,Mg,Y） and Mg2（La, Y）, respectively. A model （La, Mg,Y）0.5（La,Mg,Y）0.5 was applied to describe the compound MgM formed by MgLa and MgY in order to cope with the order-disorder transition between body-centered cubic solution （A2） and MgM with CsCl-type structure （B2） in the La-Mg-Y system. The Gibbs energies of individual phases were optimized in the La-Mg, La-Y and La-Mg-Y systems by CALPHAD technique. The projection of the liquidus surfaces for the La-Mg-Y system was predicted. The Mg-based alloys database including 36 binary and 15 ternary systems formed by Mg, Al, Cu, Ni, Mn, Zn and rare earth elements was set up in SGTE standard.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
Monte Carlo simulation of two dimensional 4 state Potts model has been carried out in microcanonical ensemble. The simulations were done on a 30 × 30 system with periodic boundary conditions. The temperature depe...Monte Carlo simulation of two dimensional 4 state Potts model has been carried out in microcanonical ensemble. The simulations were done on a 30 × 30 system with periodic boundary conditions. The temperature dependence of energy and order parameter has been calculated. The transition in 4-state Potts model is concluded to be first-order in nature. The transition temperature and latent heat of the first-order transition have been found to be 0.92 and 0.18, respectively.展开更多
We analyze systematically the effective order parameters in nuclear shape phase transition both in experiments and in the interacting boson model. We find that energy ratios and B(E2) ratios can distinguish the first ...We analyze systematically the effective order parameters in nuclear shape phase transition both in experiments and in the interacting boson model. We find that energy ratios and B(E2) ratios can distinguish the first from the second-order phase transition in theory above a certain boson number N (about 50), but in experiments, only those quantities, such as E(L1+)/E(02+) and B(E2; (L+2)1 → L1)/B(E2; 21 → 01), etc., of which the monotonous transitional behavior in the second-order phase transition is broken in the first order phase transition independent of N, are qualified as the effective order parameters. By implementing the originally proposed effective order parameters and the new ones, we find that the isotones with neutron number Nn = 62 are a trajectory of the second order phase transition. In addition, we predict that the transitional behavior of isomer shifts of Xe, Ba isotopes and Nn = 62 isotones is approximately monotonous due to the finiteness of nuclear system.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10475113
文摘A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe twoflavor normal quark matter. Depending on whether mo/A, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus mo is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value ofmo/A from QCD phenomenology, the phase transition must be of the first order.
基金This work was financially supported by the National Natural Science Foundation of China (Nos. 50471095 and 50271008).
文摘As an example of the La-Mg-Y system, the method how to set up the themaodynamic model of individual phases was introduced in the process of thermodynamic optimization. The solution phases （liquid, body-centered cubic, face-centered cubic, hexagonal close-packed and double hexagonal close-packed） were modeled with the Redlich-Kister equation. The compound energy model has been used to describe the thermodynamic functions of the intermetallic compounds in the La-Mg-Y systems. The compounds Mg2Y, Mg24Y5, Mg12La, Mg17La2, Mg41Las, Mg3La and Mg2La in the La-Mg-Y system were treated as the formulae （Mg,Y）2（La,Mg,Y）, Mg24（La,Mg,Y）4Y, Mg12（La, Y）, Mg17（La,Y）2, Mg41（La,Y）5, Mg3（La,Mg,Y） and Mg2（La, Y）, respectively. A model （La, Mg,Y）0.5（La,Mg,Y）0.5 was applied to describe the compound MgM formed by MgLa and MgY in order to cope with the order-disorder transition between body-centered cubic solution （A2） and MgM with CsCl-type structure （B2） in the La-Mg-Y system. The Gibbs energies of individual phases were optimized in the La-Mg, La-Y and La-Mg-Y systems by CALPHAD technique. The projection of the liquidus surfaces for the La-Mg-Y system was predicted. The Mg-based alloys database including 36 binary and 15 ternary systems formed by Mg, Al, Cu, Ni, Mn, Zn and rare earth elements was set up in SGTE standard.
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.
文摘Monte Carlo simulation of two dimensional 4 state Potts model has been carried out in microcanonical ensemble. The simulations were done on a 30 × 30 system with periodic boundary conditions. The temperature dependence of energy and order parameter has been calculated. The transition in 4-state Potts model is concluded to be first-order in nature. The transition temperature and latent heat of the first-order transition have been found to be 0.92 and 0.18, respectively.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10425521, 10935001, 11005056 and 11075052)the Major State Basic Research Development Program (Grant No.G2007CB815000)
文摘We analyze systematically the effective order parameters in nuclear shape phase transition both in experiments and in the interacting boson model. We find that energy ratios and B(E2) ratios can distinguish the first from the second-order phase transition in theory above a certain boson number N (about 50), but in experiments, only those quantities, such as E(L1+)/E(02+) and B(E2; (L+2)1 → L1)/B(E2; 21 → 01), etc., of which the monotonous transitional behavior in the second-order phase transition is broken in the first order phase transition independent of N, are qualified as the effective order parameters. By implementing the originally proposed effective order parameters and the new ones, we find that the isotones with neutron number Nn = 62 are a trajectory of the second order phase transition. In addition, we predict that the transitional behavior of isomer shifts of Xe, Ba isotopes and Nn = 62 isotones is approximately monotonous due to the finiteness of nuclear system.
