We numerically investigate the quenched random directed sandpile models which are local, conservative and Abelian. A local flow balance between the outflow of grains during a single toppling at a site and the total nu...We numerically investigate the quenched random directed sandpile models which are local, conservative and Abelian. A local flow balance between the outflow of grains during a single toppling at a site and the total number of grains flowing into the same site plays an important role when all the nearest-neighbouring sites of the above-mentioned site topple for once. The quenched model has the same critical exponents with the Abelian deterministic directed sandpile model when the local flow balance exists, otherwise the critical exponents of this quenched model and the annealed Abelian random directed sandpile model are the same. These results indicate that the presence or absence of this local flow balance determines the universality class of the Abelian directed sandpile model.展开更多
The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approxi...The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.展开更多
For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the external magnetic field of site i in this model depend on the coordinatio...For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the external magnetic field of site i in this model depend on the coordination number qi of site i, and that the relation $b_{q_i}/b_{q_j} = q{_i}/q{_j}$ holds among bq's, where bq is the Gaussian type distribution constant of site j. Using the decimation real-space renormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierarchical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site j can be expressed in the form $K^* = b{_q }_{_i } /q{_i } and h_{q_j }^* = 0$ respectively. It is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices, and if the fractal dimensionalityd f=4, the Gaussian model and the mean field theories give the same results.展开更多
We investigate the bound states of the Yukawa potential V(r)=-λexp(-αr)/r, using different algorithms: solving the Schrodinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = ...We investigate the bound states of the Yukawa potential V(r)=-λexp(-αr)/r, using different algorithms: solving the Schrodinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = αC, above which no bound state exists. We study the relation between αC and A for various angular momentum quantum number l. and find in atomic units, αC(l) = λ[A1 exp(-l/B1) + A2exp(-l/B2)], with A1 = 1.020(18), B1 = 0.443(14), A2 = 0.170(17), and B2 = 2.490(180).展开更多
The critical behavior of pseudobinary microemulsion systems{water/sodium di(2-ethylhexyl)sulfo- succinate(AOT)/n-decane}with various droplet sizes was studied by measurements of refractive index. It was found that the...The critical behavior of pseudobinary microemulsion systems{water/sodium di(2-ethylhexyl)sulfo- succinate(AOT)/n-decane}with various droplet sizes was studied by measurements of refractive index. It was found that the critical exponentsβfor all systems approach 0.327 in a region sufficiently close to the critical temperature,which is consistent with 3D-Ising universality class.The critical temperatures linearly decrease as the dispersed droplet sizes increase.The critical amplitude almost linearly in- creases with increasing the dispersed droplet sizes.展开更多
文摘We numerically investigate the quenched random directed sandpile models which are local, conservative and Abelian. A local flow balance between the outflow of grains during a single toppling at a site and the total number of grains flowing into the same site plays an important role when all the nearest-neighbouring sites of the above-mentioned site topple for once. The quenched model has the same critical exponents with the Abelian deterministic directed sandpile model when the local flow balance exists, otherwise the critical exponents of this quenched model and the annealed Abelian random directed sandpile model are the same. These results indicate that the presence or absence of this local flow balance determines the universality class of the Abelian directed sandpile model.
文摘The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.
基金澳大利亚研究委员会(ARC)基金——The Lexicon Project:Analysing pedagogical naming systems from different cultures to reconceptualise classroom practice and advance educational theory(DP140101361)
基金澳大利亚研究委员会(ARC)基金--The Lexicon Project:Analysing Pedagogical Naming Systems from Different Cultures to Reconceptualise Classroom Practice and Advance Educational Theory(编号:DP140101361)的研究成果
文摘For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the external magnetic field of site i in this model depend on the coordination number qi of site i, and that the relation $b_{q_i}/b_{q_j} = q{_i}/q{_j}$ holds among bq's, where bq is the Gaussian type distribution constant of site j. Using the decimation real-space renormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierarchical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site j can be expressed in the form $K^* = b{_q }_{_i } /q{_i } and h_{q_j }^* = 0$ respectively. It is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices, and if the fractal dimensionalityd f=4, the Gaussian model and the mean field theories give the same results.
基金the National Natural Science Foundation of China (Grant No. 10235040) the Education Ministry of China (Grant No. 105135)+1 种基金 Chinese Academy of Sciences (Grant No. KJCX2-SW-N10) Guangdong Provincial Natural Science Foundation (Grant No. 05101821).
文摘We investigate the bound states of the Yukawa potential V(r)=-λexp(-αr)/r, using different algorithms: solving the Schrodinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = αC, above which no bound state exists. We study the relation between αC and A for various angular momentum quantum number l. and find in atomic units, αC(l) = λ[A1 exp(-l/B1) + A2exp(-l/B2)], with A1 = 1.020(18), B1 = 0.443(14), A2 = 0.170(17), and B2 = 2.490(180).
基金Supported by the National Natural Science Foundation of China(Grant Nos.20673059,20273032,20473035 and 20573056)the New Technique Foundation of Jiangsu Province,China(Grant No.BG-2005041)and the Special Sustentation Fundof Nanometer Technology of Shanghai City,China(Grant No.0652nm010)
文摘The critical behavior of pseudobinary microemulsion systems{water/sodium di(2-ethylhexyl)sulfo- succinate(AOT)/n-decane}with various droplet sizes was studied by measurements of refractive index. It was found that the critical exponentsβfor all systems approach 0.327 in a region sufficiently close to the critical temperature,which is consistent with 3D-Ising universality class.The critical temperatures linearly decrease as the dispersed droplet sizes increase.The critical amplitude almost linearly in- creases with increasing the dispersed droplet sizes.
