四维伊辛模型总磁化强度的微扰PDF
Perturbative PDF of the total magnetization of the 4D Ising model
摘要：
本文用微扰论方法计算了伊辛模型在4-环面和4-球面上的总磁化概率密度函数$M$。我们开发了一个单一的微扰膨胀，是有效的对称相以及对称性破缺相，只要相关长度是大的系统大小相比，$L$。我们发现，在临界点处，对于晶格单元中的大系统尺寸，PDF接近$p(M)\sim \exp(-f(L) M^4)$。因此，总磁化强度的Binder累积量的临界值是$U = 1 - \frac{4\,Γ(5/4)^2}{3\,Γ(3/4)^2}$。我们通过与蒙特卡罗模拟的比较来验证我们的结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
