The mean-field theory has been considered as applied to the system of magnetic and nonmagnetic atoms at thermal equilibrium. The phase diagrams and the dependence of the magnetization on the density of magnetic atoms have been found in the Ising model with mobile nonmagnetic impurities. In the ...
接下来这篇文章把半监督学习问题用 Ising 模型来建模,并且使用平均场方法(naive mean field approach)来解决。文章还指出,贝叶斯方法和该方法在本质上的联系;特别地,半监督学习问题的本质就是要利用数据标签在数据空间上的平滑特性,可以把数据空间建模为一个图(graph),这又和我们前面在研究的 spectral graph theory ...
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in $d\\le 2$ space ...
Mean-Field Theory II: Exact Solution in Infinite Dimensionstatistical mechanicsinteracting systemsmean-field theoryexact solution in infinite dimensioninfinite-range ising modelinfinite-range classical gasdoi:10.1002/3527603158.ch11Chowdhury, Debashish
The macroscopic parameter of population imbalance σz in laser theory plays a role of reciprocal temperature β, which is relevant to the whole system characterization for the Ising model16. Noteworthy, σz,thr vanishes for large average node degree ⟨k⟩. In this sense the solaser represents...
The need for the Ising model in Mean field theory? https://physics.stackexchange.com/questions/335562/the-need-for-the-ising-model-in-mean-field-theory You are correct when saying thatmj=⟨Sj⟩is not necessarily aligned withB. We can write your second equation asHi=−JSi...
Although these methods are very general and can also be used to study quantum mechanical many-body systems 1 , for our purpose it is sufficient to introduce these methods using the nearest-neighbor Ising model in D dimensions as an example....
The semi-infinite Ising model, for S=(1/2) and with an arbitrary number of surface magnetic couplings Jdifferent from the bulk J, is solved in the mean-field approximation. Exact expressions for the critical couplings J,C leading to a surface Curie temperature Thigher than the bulk Tare ob...
realistic Heisenberg model in which all three of the components of the spin appear. Despite its simplicity, the Ising model is very difficult to solve exactly. There is, however, an approximation, the mean field theory, which gives a good qualitative description of ferromagnetism. The idea ...
Generalization of the Maier-Saupe theory of the nematics within Tsa llis Thermostatistics In this study, one of the mean-field theories in nematics, the Maier鈥揝aupe theory (MST), is generalized within Tsallis thermostatistics (TT). The variati... O Kayacan,F. Büyükkl,D Demirhan - 《...