关于临界点附近平均场理论的失效
On the failure of mean-field theories near a critical point
AI总结：
本研究挑战平均场理论因涨落发散失效的传统观点，指出涨落发散是统计独立性破缺的结果且可被平均场理论复现，其失效本质是未能捕捉临界点附近序参量的长程标度平均效应。
摘要：
众所周知，平均场理论无法复现实验测得的临界指数。解释临界点附近平均场理论失效的传统论据是金兹堡（Ginsburg）判据，该判据认为序参量的涨落发散是根本原因。我们与上述传统观点相反，认为真实物理系统在临界点附近的涨落发散是统计独立性性质破缺的真实结果，且能被平均场理论忠实地复现。从“统计独立性”的视角看待这一问题，真实物理系统在临界态附近的涨落发散会变得一目了然，因为可以在发散的关联长度与发散的涨落之间建立联系。为解答为何在定性层面十分成功的平均场理论无法复现已知的临界指数值这一问题，我们利用威耳逊（Wilsonian）重整化群的核心思想提出，平均场理论未能捕捉到临界点附近序参量的长程长度标度平均效应。
英文摘要：
It is well known that mean-field theories fail to reproduce the experimentally known critical exponents. The traditional argument which explain this failure of mean-field theories near a critical point is the Ginsburg criterion in which diverging fluctuations of the order parameter is the root cause. We argue, contrary to the above mentioned traditional view, that diverging fluctuations in real physical systems near a critical point are genuine consequence of the breakdown of the property of statistical independence, and are faithfully reproduced by the mean-field theory. By looking at the problem from the point of view of "statistical independence" the divergence of fluctuations in real physical systems near criticality becomes immediately apparent as a connection can be established between diverging correlation length and diverging fluctuations. To address the question of why mean-field theories, much successful qualitatively, fail to reproduce the known values of critical indices we argue, using the essential ideas of the Wilsonian renormalization group, that mean-field theories fail to capture the long length scale averages of an order parameter near a critical point.
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。
