We explore the Potts model on the generalized decorated square lattice,with both nearest(J1)and next-nearest(J2)neighbor interactions.Using the tensor renormalization-group method augmented by higher order singular va...We explore the Potts model on the generalized decorated square lattice,with both nearest(J1)and next-nearest(J2)neighbor interactions.Using the tensor renormalization-group method augmented by higher order singular value decompositions,we calculate the spontaneous magnetization of the Potts model with q=2,3,and 4.The results for q=2 allow us to benchmark our numerics using the exact solution.For q=3,we find a highly degenerate ground state with partial order on a single sublattice,but with vanishing entropy per site,and we obtain the phase diagram as a function of the ratio J2/J1.There is no finite-temperature transition for the q=4 case when J1=J2,whereas the magnetic susceptibility diverges as the temperature goes to zero,showing that the model is critical at T=0.展开更多
The stabilization and H∞ control of nonlinear differential algebraic systems （NDAS） are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization （DHR...The stabilization and H∞ control of nonlinear differential algebraic systems （NDAS） are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization （DHR） structure and give the condition to complete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10934008,10874215 and 11174365the National Basic Research Program of China under Grant Nos 2012CB921704 and 2011CB309703.
文摘We explore the Potts model on the generalized decorated square lattice,with both nearest(J1)and next-nearest(J2)neighbor interactions.Using the tensor renormalization-group method augmented by higher order singular value decompositions,we calculate the spontaneous magnetization of the Potts model with q=2,3,and 4.The results for q=2 allow us to benchmark our numerics using the exact solution.For q=3,we find a highly degenerate ground state with partial order on a single sublattice,but with vanishing entropy per site,and we obtain the phase diagram as a function of the ratio J2/J1.There is no finite-temperature transition for the q=4 case when J1=J2,whereas the magnetic susceptibility diverges as the temperature goes to zero,showing that the model is critical at T=0.
基金the National Natural Science Foundation of China （Grant Nos. 69774011 and 60433050）.
文摘The stabilization and H∞ control of nonlinear differential algebraic systems （NDAS） are investigated using the Hamiltonian function method. Firstly, we put forward a novel dissipative Hamiltonian realization （DHR） structure and give the condition to complete the Hamiltonian realization. Then, based on the DHR, we present a criterion for the stability analysis of NDAS and construct a stabilization controller for NDAS in absence of disturbances. Finally, for NDAS in presence of disturbances, the L2 gain is analyzed via generalized Hamilton-Jacobi inequality and an H∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of NDAS and is simple in form.
