二维自旋系统aging现象的数值模拟研究

应用动力学蒙特卡罗模拟方法，对二维Ising模型和二维XY模型的aging现象展开数值研究.系统在零外场条件下从高温无序相淬火到临界温度T_c时，通过测量自关联函数A(t,t′)，观察到二维Ising模型和二维XY模型的aging现象，获得更精确的动力学临界指数λ_c和z的值.特别是对二维XY模型，当初始态为完全无序态时，模拟结果证实存在关于标度行为的对数修正. 关键词： 蒙特卡罗模拟 相变和临界行为 aging现象     

二层Ising模型的短时临界动力学性质

采用动力学Monte Carlo 方法研究了二层Ising模型的临界性质及早期动力学标度行为.结果表明层间耦合不为零时也存在临界点;计算了早期动力学临界指数θ;估计了传统的临界指数1/νz.其结果支持临界线存在的猜想,并表明此模型很可能是一种弱普适模型. 关键词：     

二维３态Potts量子系统的保真度与序参量

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态 (iPEPS) 算法,在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于iPEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.     

二维３态Potts量子系统的保真度与序参量

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态算法(iPEPS),在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还开创性提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于iPEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.     

二维3态Potts量子系统的保真度与序参量

二维无限正方格子上的量子3态Potts模型是发生一级相变还是二级相变?通过运用无限纠缠投影对态(i PEPS)算法,在进行数值模拟时任意选取初态,能得到二维无限正方格子上的3态Potts模型的三个不同的简并基态波函数,这些简并的情况是由自发对称性破缺引起的.首先,揭示了在二维系统中自发对称性破缺引起的相变可以运用单点基态保真度的分叉来研究,也反映了在二维系统中约化保真度同样有一个分叉行为;再者,还提出了二维系统的普适序参量以及多分量的复数局域序参量的行为来尝试研究二维3态Potts模型,共同确定系统发生的量子相变的临界点及其类型.即基于i PEPS算法,从单点基态保真度、约化保真度、普适序参量以及局域序参量的角度,来研究3态Potts模型的量子相变,其为一级相变.     

二维伊辛模型的畴壁动力学

表面可以改变纳米磁性薄膜的结构和相变温度，畴壁动力学由此成为研究的重点。本文采用动力学蒙特卡罗模拟方法，对二维Ising模型磁畴界面的非平衡动力学展开数值研究。系统初态设为半正半负，即由完全有序但自旋取向完全相反的两部分组成，其间的磁畴壁随时间生长。通过对磁化标度形式的分析，发现畴壁内外的动力学标度形式虽然相同，但临界指数在数值上却存在很大差异，相差一个 =1，这是由初始条件导致的。     

二维完全阻挫XY模型的动力学指数

采用大规模动力学蒙特卡罗模拟方法,对二维完全阻挫XY模型的Kosterlitz-Thouless(KT)型相变展开数值研究.系统从有序初始态出发演化到高于KT相变的温度,以普适的动力学标度形式为基础,通过测量磁化和Binder累积量,得出动力学关联时间和平衡态空间关联长度,确定出更精确的动力学指数z.特别是建议并证实了一种在KT相变温度以上(T>TKT),独立判断动力学指数z的方法.模拟结果表明,动力学指数z≈2,这与在相变温度以下(T     

二维完全阻挫$lt;i$gt;XY$lt;/i$gt;模型的动力学指数

采用大规模动力学蒙特卡罗模拟方法,对二维完全阻挫XY模型的Kosterlitz-Thouless（KT）型相变展开数值研究.系统从有序初始态出发演化到高于KT相变的温度,以普适的动力学标度形式为基础,通过测量磁化和Binder累积量,得出动力学关联时间和平衡态空间关联长度,确定出更精确的动力学指数z.特别是建议并证实了一种在KT相变温度以上（T>T_KT）,独立判断动力学指数z的方法.模拟结果表明,动力学指数z≈2,这与在相变温度以下（T<T_KT）测量的结果一致. 关键词： 蒙特卡罗法 动力学指数 Kosterlitz-Thouless相变 XY模型')" href="#">二维完全阻挫XY模型     

二维随机三角点阵上三态和四态Potts模型的蒙特—卡罗重整化群研究

本文用改进的蒙特-卡罗重整化群方法对二维随机三角点阵上的三态和四态Potts模型进行研究,分析它们的固定点及临界指数,所得的临界指数与理论的分析值符合很好。     

二维伊辛模型的畴壁动力学

表面可以改变纳米磁性薄膜的结构和相变温度,畴壁动力学由此成为研究的重点.本文采用动力学蒙特卡罗模拟方法,对二维Ising模型磁畴界面的非平衡动力学展开数值研究.系统初态设为半正半负,即由完全有序但自旋取向完全相反的两部分组成,其间的磁畴壁随时间生长.通过对磁化标度形式的分析,发现畴壁内外的动力学标度形式虽然相同,但临界...     

Short-Time Dynamics of Random-Bond Potts Ferromagnet with Continuous Self-Dual Quenched Disorders

We present our Monte Carlo results of the random-bond Potts ferromagnet with the Olson-Young self-dual distribution of quenched disorders in two dimensions. By exploring the short-time scaling dynamics, we find the universal power-law critical behavior of the magnetization and Binder cumulant at the critical point, and thus obtain estimates of the dynamic exponent z and magnetic exponent η, as well as the exponent θ. Our special attention is paid to the dynamic process for the q = 8 Potts model.     

Model for domain wall avalanches in ferromagnetic thin films

The Barkhausen jumps or avalanches in magnetic domain-walls motion between successive pinned configurations, due the competition among magnetic external driving force and substrum quenched disorder, appear in bulk materials and thin films. We introduce a model based in rules for the domain wall evolution of ferromagnetic media with exchange or short-range interactions, that include disorder and driving force effects. We simulate in 2-dimensions with Monte Carlo dynamics, calculate numerically distributions of sizes and durations of the jumps and find power-law critical behavior. The avalanche-size exponent is in excellent agreement with experimental results for thin films and is close to predictions of the other models, such as like random-field and random-bond disorder, or functional renormalization group. The model allows us to review current issues in the study of avalanches motion of the magnetic domain walls in thin films with ferromagnetic interactions and opens a new approach to describe these materials with dipolar or long-range interactions.     

Critical behaviour of random-bond Potts models: a transfer matrix study

We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q > 4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting universality classes by combining transfer matrix data with conformal invariance. The magnetic exponent β/v varies continuously with q, assuming non-Ising values for q > 4, whereas the correlation length exponent ν is numerically consistent with unity. We present evidence for the correctness of a formerly proposed phase diagram, unifying pure, percolative and non-trivial random behaviour.     

The energy of the spin-glass state of a binary mixture at T = 0 and its variational properties

In the random-bond model of Ising spins, the concept of a multiple-bond distribution of effective field was introduced in the pair approximation. The integral equation for a single-bond distribution was derived intuitively. The variational energy at T = 0 is expressed in terms of two parameters μ and η where μ is the probability of zero effective field in the single-bond distribution and η is the magnetization per spin. For η = 0, the energy of the spin-glass state corresponds to a local minimum as a function of μ, for an even z (number of the nearest neighbours) and to an inflection point for an odd z. It was shown that the spin-glass state corresponds to a local minimum with respect to μ and η for z = 4, to an inflection point with respect to μ and a local minimum with respect to η for z = 3. It is conjectured that the maximum of the energy of the spin-glass state of Sherrington and Kirkpatrick is attributed not to the replica method, but to the mean field approximation. Stationary properties of the energy as a function of both μ and η were examined in detail.     

Wang-Landau study of the 3D Ising model with bond disorder

We implement a two-stage approach of the Wang-Landau algorithm to investigate the critical properties of the 3D Ising model with quenched bond randomness. In particular, we consider the case where disorder couples to the nearest-neighbor ferromagnetic interaction, in terms of a bimodal distribution of strong versus weak bonds. Our simulations are carried out for large ensembles of disorder realizations and lattices with linear sizes L in the range L=8-64L=8{-}64. We apply well-established finite-size scaling techniques and concepts from the scaling theory of disordered systems to describe the nature of the phase transition of the disordered model, departing gradually from the fixed point of the pure system. Our analysis (based on the determination of the critical exponents) shows that the 3D random-bond Ising model belongs to the same universality class with the site- and bond-dilution models, providing a single universality class for the 3D Ising model with these three types of quenched uncorrelated disorder.     

Probability distributions for the overlaps and self-correlations of the pure states of ann-vector model

The probability distributions for the overlaps between and the self-correlations of the pure states of the Stanleyn-vector model with infinite-range interactions are derived. These probability distributions represent two new order parameters for the model and are intimately related to the parameters which arise naturally within the replica formalism for the treatment of the corresponding quenched random-bond model. In contrast to then = 1 Ising case, the probability distributions are nontrivial whenn > 1 and an additional parameter for self-correlation has to be introduced.     

Chiral ordering in the four-dimensional planar spin glass

The chiral glass behaviour of the nearest-neighbour random-bond XY spin glass in four dimensions is studied by Monte Carlo simulations. A chiral glass transition at T _cg = 0:90 ± 0:05 is found by a finite-size scaling analysis of the results. The associated chiral correlation-length exponent is estimated to be gv _cg = 0:6±0:1. Both values are very similar to those reported recently for the spin glass transition in this model. The results strongly suggest a simultaneous ordering of spin and chirality in four dimensions.     

Correlated correlation functions in random-bond ferromagnets

The two-dimensional random-bond Q-state Potts model is studied for Q near 2 via the perturbative renormalisation group to one loop. It is shown that weak disorder induces cross-correlations between the quenched-averages of moments of the two-point spin/spin and energy/energy correlation functions, which should be observable numerically in specific linear combinations of various quenched correlation functions. The random-bond Ising model in (2+ε) dimensions is similarly treated. As a byproduct, a simple method for deriving the scaling dimensions of all moments of the local energy operator is presented.     

Maximum Renyi entropy principle for systems with power-law Hamiltonians

The Renyi distribution ensuring the maximum of Renyi entropy is investigated for a particular case of a power-law Hamiltonian. Both Lagrange parameters alpha and beta can be eliminated. It is found that beta does not depend on a Renyi parameter q and can be expressed in terms of an exponent kappa of the power-law Hamiltonian and an average energy U. The Renyi entropy for the resulting Renyi distribution reaches its maximal value at q=1/(1+kappa) that can be considered as the most probable value of q when we have no additional information on the behavior of the stochastic process. The Renyi distribution for such q becomes a power-law distribution with the exponent -(kappa+1). When q=1/(1+kappa)+epsilon (0相似文献   

The chiral magnetic effect and chiral symmetry breaking in <Emphasis Type="Italic">SU</Emphasis>(3) quenched lattice gauge theory

We study some properties of the non-Abelian vacuum induced by strong external magnetic field. We perform calculations in the quenched SU(3) lattice gauge theory with tadpole-improved Lüscher-Weisz action and chirally invariant lattice Dirac operator. The following results are obtained: The chiral symmetry breaking is enhanced by the magnetic field. The chiral condensate depends on the strength of the applied field as a power function with exponent ν = 1.6 ± 0.2. There is a paramagnetic polarization of the vacuum. The corresponding susceptibility and other magnetic properties are calculated and compared with the theoretical estimations. There are nonzero local fluctuations of the chirality and electromagnetic current, which grow with the magnetic field strength. These fluctuations can be a manifestation of the Chiral Magnetic Effect.