论文标题
与四分之一相互作用的3D晶格费米模型的手性临界行为
Chiral critical behavior of 3D lattice fermionic models with quartic interactions
论文作者
论文摘要
我们研究具有$ n_f $ dirac fermionic口味和四个互动的三维（3D）GROSS-NEVEU（GN）模型的临界行为，在手性$ {\ Mathbb Z} _2 _2 $ the basseless $ {\ mathbb z} _2 $ the basseless $ {\ mathbb z} _2 $ the boss $ {\ mathbb z} _2 _2 _2 _2 _2 $ - symemmetr-symmetrim metrip limem中。为此，我们考虑了一个带有交错的Kogut-susskind费米子和标量耦合到标量双线性费米子操作员的标量场的晶格GN模型，该模型有效地实现了有吸引力的四边形相互作用。我们以$ n_f = 4,8,12,16 $进行蒙特卡洛（MC）模拟。通过对数值数据的有限尺寸缩放分析，我们获得了与使用Continuum GN Field理论获得的大型$ N_F $预测相比的关键指数的估计。我们观察到一个实质性的协议。这证实了带有交错费用的晶格GN模型，即使晶格相互作用明确打破了gn量的风味$ {\ rm u}（n_f）\ outimes {\ rm um u}（n_f）（n_f）$ symmetry of gn of gn offimimition fircountion fircountion fircountion recounted recounted recounted，gn量子量相互作用均未实现GN量子场理论的非企业实现。
We study the critical behavior of the three-dimensional (3D) Gross-Neveu (GN) model with $N_f$ Dirac fermionic flavors and quartic interactions, at the chiral ${\mathbb Z}_2$ transition in the massless ${\mathbb Z}_2$-symmetric limit. For this purpose, we consider a lattice GN model with staggered Kogut-Susskind fermions and a scalar field coupled to the scalar bilinear fermionic operator, which effectively realizes the attractive four-fermion interaction. We perform Monte Carlo (MC) simulations for $N_f=4,8,12,16$. By means of finite-size scaling analyses of the numerical data, we obtain estimates of the critical exponents that are compared with the large-$N_f$ predictions obtained using the continuum GN field theory. We observe a substantial agreement. This confirms that lattice GN models with staggered fermions provide a nonpertubative realization of the GN quantum field theory, even though the lattice interactions explicitly break the flavor ${\rm U}(N_f)\otimes {\rm U}(N_f)$ symmetry of the GN field theory, which is only recovered in the critical limit.
