The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictio...The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.展开更多
We investigate the area distribution of clusters (loops) in the honeycomb O(n) loop model by means of the worm algorithm with n = 0.5, 1, 1.5, and 2. At the critical point, the number of clusters, whose enclosed area ...We investigate the area distribution of clusters (loops) in the honeycomb O(n) loop model by means of the worm algorithm with n = 0.5, 1, 1.5, and 2. At the critical point, the number of clusters, whose enclosed area is greater than A, is proportional to A-1 with a proportionality constant C. We confirm numerically that C is universal, and its value agrees well with the predictions based on the Coulomb gas method.展开更多
We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations,using an efficient cluster algorithm and a finite-size scaling analysis.The critical points and four critical expo...We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations,using an efficient cluster algorithm and a finite-size scaling analysis.The critical points and four critical exponents of the model are determined for several values of n.Two of the exponents are fractal dimensions,which are obtained numerically for the first time.Our results are consistent with the Coulomb gas predictions for the critical O(n) branch for n < 2 and the results obtained by previous transfer matrix calculations.For n=2,we find that the thermal exponent,the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model.These results confirm that the cubic anisotropy is marginal at n=2 but irrelevant for n < 2.展开更多
The upper critical dimension of the Ising model is known to be dc=4,above which critical behavior is regarded to be trivial.We hereby argue from extensive simulations that,in the random-cluster representation,the Isin...The upper critical dimension of the Ising model is known to be dc=4,above which critical behavior is regarded to be trivial.We hereby argue from extensive simulations that,in the random-cluster representation,the Ising model simultaneously exhibits two upper critical dimensions at(d_(c)=4,d_(p)=6),and critical clusters for d≥d_(p),except the largest one,are governed by exponents from percolation universality.We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs.Our findings significantly advance the understanding of the Ising model,which is a fundamental system in many branches of physics.展开更多
基金Project supported by the Hefei National Research Center for Physical Sciences at the Microscale (Grant No.KF2021002)the Natural Science Foundation of Shanxi Province,China (Grant Nos.202303021221029 and 202103021224051)+2 种基金the National Natural Science Foundation of China (Grant Nos.11975024,12047503,and 12275263)the Anhui Provincial Supporting Program for Excellent Young Talents in Colleges and Universities (Grant No.gxyq ZD2019023)the National Key Research and Development Program of China (Grant No.2018YFA0306501)。
文摘The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10975127)the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20113402110040)
文摘We investigate the area distribution of clusters (loops) in the honeycomb O(n) loop model by means of the worm algorithm with n = 0.5, 1, 1.5, and 2. At the critical point, the number of clusters, whose enclosed area is greater than A, is proportional to A-1 with a proportionality constant C. We confirm numerically that C is universal, and its value agrees well with the predictions based on the Coulomb gas method.
基金Project supported by the National Natural Science Foundation of China (Grant No.10675021)the New Century Excellent Talents in University of China,the Natural Science Foundation of Anhui Province of China (Grant No.090416224)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20103402110053)
文摘We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations,using an efficient cluster algorithm and a finite-size scaling analysis.The critical points and four critical exponents of the model are determined for several values of n.Two of the exponents are fractal dimensions,which are obtained numerically for the first time.Our results are consistent with the Coulomb gas predictions for the critical O(n) branch for n < 2 and the results obtained by previous transfer matrix calculations.For n=2,we find that the thermal exponent,the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model.These results confirm that the cubic anisotropy is marginal at n=2 but irrelevant for n < 2.
文摘The upper critical dimension of the Ising model is known to be dc=4,above which critical behavior is regarded to be trivial.We hereby argue from extensive simulations that,in the random-cluster representation,the Ising model simultaneously exhibits two upper critical dimensions at(d_(c)=4,d_(p)=6),and critical clusters for d≥d_(p),except the largest one,are governed by exponents from percolation universality.We predict a rich variety of geometric properties and then provide strong evidence in dimensions from 4 to 7 and on complete graphs.Our findings significantly advance the understanding of the Ising model,which is a fundamental system in many branches of physics.
基金supported by the National Natural Science Foundation of China (11874340)the National Key R&D Program of China (2018YFA0306501)+2 种基金the CASthe Anhui Initiative in Quantum Information Technologiesthe Fundamental Research Funds for the Central Universities (WK2340000081)
