论文标题
4D ISING模型的总磁化的扰动PDF
Perturbative PDF of the total magnetization of the 4D Ising model
论文作者
论文摘要
我们在扰动理论的一个循环中计算了4个螺旋和4-Sphere上伊辛模型的总磁化$ m $的概率密度函数。我们开发了一个单一的扰动扩展，该扩展在对称阶段以及损坏的对称阶段是有效的，前提是与系统尺寸$ l $相比，相关长度很大。我们发现，在关键点，对于晶格单元中的大型系统大小，PDF接近$ p（m）\ sim \ exp（-f（l）m^4）$。因此，总磁化的粘合剂累积的临界值为$ u = 1 - \ frac {4 \，γ（5/4）^2} {3 \，γ（3/4）^2} $。我们通过与蒙特卡洛模拟进行比较来验证结果。
We compute, at one loop in perturbation theory, the probability density function of the total magnetization $M$ of the Ising model on the 4-torus and the 4-sphere. We develop a single perturbative expansion that is valid in the symmetric phase as well as the broken symmetry phase, provided that the correlation length is large compared to the system size $L$. We find that, at the critical point, for large system size in lattice units, the PDF approaches $p(M)\sim \exp(-f(L) M^4)$. Consequently, the critical value of the Binder cumulant of the total magnetization is $U = 1 - \frac{4\,Γ(5/4)^2}{3\,Γ(3/4)^2}$. We validate our results by comparison with Monte Carlo simulation.
