We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix and finite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb lattice w...We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix and finite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb lattice with vacancies; the tricritical behavior is associated with the percolation threshold of the vacancies. The vacancies are represented by face variables on the elementary hexagons of thelattice. We apply a mapping of the spin degrees of freedom model on a non-intersecting-loop model, in which the number n of spin components assumes the role of a continuously variable parameter. This loop model serves as a suitable basis for the construction of the transfer matrix.Our results reveal the existence of a tricritical line, parametrized by n, which connects the known universality classes of the tricritical Ising model and the theta point describing the collapse of a polymer. On the other side of theIsing point,the tricritical line extends to the n = 2 point describing a tricritical O(2) model.展开更多
Bulk density(BD) is an important soil physical property and has significant effect on soil water conservation function. Indirect methods, which are called pedotransfer functions(PTFs), have replaced direct measurement...Bulk density(BD) is an important soil physical property and has significant effect on soil water conservation function. Indirect methods, which are called pedotransfer functions(PTFs), have replaced direct measurement and can acquire the missing data of BD during routine soil surveys. In this study, multiple linear regression(MLR) and artificial neuron network(ANN) methods were used to develop PTFs for predicting BD from soil organic carbon(OC), texture and depth in the Three-River Headwater region of Qinghai Province, China. The performances of the developed PTFs were compared with 14 published PTFs using four indexes, the mean error(ME), standard deviation error(SDE), root mean squared error(RMSE) and coefficient of determination(R^2). Results showed that the performances of published PTFs developed using exponential regression were better than those developed using linear regression from OC. Alexander(1980)-B, Alexander(1980)-A and Manrique and Jones(1991)-B PTFs, which had good predictions, could be applied for the soils in the study area. The PTFs developed using MLR(MLR-PTFs) and ANN(ANN-PTFs) had better soil BD predictions than most of published PTFs. The ANN-PTFs had better performances than the MLR-PTFs and their performances could be improved when soil texture and depth were added as predictor variables. The idea of developing PTFs for predicting soil BD in the study area could provide reference for other areas and the results could lay foundation for the estimation of soil water retention and carbon pool.展开更多
文摘We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix and finite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb lattice with vacancies; the tricritical behavior is associated with the percolation threshold of the vacancies. The vacancies are represented by face variables on the elementary hexagons of thelattice. We apply a mapping of the spin degrees of freedom model on a non-intersecting-loop model, in which the number n of spin components assumes the role of a continuously variable parameter. This loop model serves as a suitable basis for the construction of the transfer matrix.Our results reveal the existence of a tricritical line, parametrized by n, which connects the known universality classes of the tricritical Ising model and the theta point describing the collapse of a polymer. On the other side of theIsing point,the tricritical line extends to the n = 2 point describing a tricritical O(2) model.
基金supported by the National Key Technology R&D Program of China(No.2009BAC61B01)the National Basic Research Program(973Program) of China(No.2012CB95570002)the Innovative Team(Investigation and Management for Agricultural Land Resource) of Predominant Science and Technology in Chinese Academy of Agricultural Engineering
文摘Bulk density(BD) is an important soil physical property and has significant effect on soil water conservation function. Indirect methods, which are called pedotransfer functions(PTFs), have replaced direct measurement and can acquire the missing data of BD during routine soil surveys. In this study, multiple linear regression(MLR) and artificial neuron network(ANN) methods were used to develop PTFs for predicting BD from soil organic carbon(OC), texture and depth in the Three-River Headwater region of Qinghai Province, China. The performances of the developed PTFs were compared with 14 published PTFs using four indexes, the mean error(ME), standard deviation error(SDE), root mean squared error(RMSE) and coefficient of determination(R^2). Results showed that the performances of published PTFs developed using exponential regression were better than those developed using linear regression from OC. Alexander(1980)-B, Alexander(1980)-A and Manrique and Jones(1991)-B PTFs, which had good predictions, could be applied for the soils in the study area. The PTFs developed using MLR(MLR-PTFs) and ANN(ANN-PTFs) had better soil BD predictions than most of published PTFs. The ANN-PTFs had better performances than the MLR-PTFs and their performances could be improved when soil texture and depth were added as predictor variables. The idea of developing PTFs for predicting soil BD in the study area could provide reference for other areas and the results could lay foundation for the estimation of soil water retention and carbon pool.
