Lundow P H, Markström K
Department of Theoretical Physics, KTH, SE-106 91 Stockholm, Sweden.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031104. doi: 10.1103/PhysRevE.80.031104. Epub 2009 Sep 3.
In this paper we investigate the nature of the singularity of the Ising model of the four-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent alpha=0 but a nonrigorous field-theory argument predicts an unbounded specific heat with a logarithmic singularity at Tc. We find that within the given accuracy the canonical ensemble data are consistent both with a logarithmic singularity and a bounded specific heat but that the microcanonical ensemble lends stronger support to a bounded specific heat. Our conclusion is that either much larger system sizes are needed for Monte Carlo studies of this model in four dimensions or the field-theory prediction of a logarithmic singularity is wrong.
在本文中，我们研究了四维立方晶格伊辛模型奇点的性质。已知比热的临界指数α = 0，但一个非严格的场论论证预测在Tc处比热无界且具有对数奇点。我们发现，在给定精度内，正则系综数据与对数奇点和有界比热均一致，但微正则系综更支持有界比热。我们的结论是，对于该四维模型的蒙特卡罗研究，要么需要大得多的系统规模，要么场论中对数奇点的预测是错误的。
