Schwinger-Dyson equation of a Wilson loop and the phase structure of SU(2) lattice gauge theory

The Schwinger-Dyson equation of a Wilson loop is used to study the phase structure of the SU(2) lattice gauge system. It is shown that there is no evidence of a phase transition in the four-dimensional case, while there is a deconfinement phase transition in the five-dimensional case.     

On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume

We study the scaling behavior of the two-flavor chiral phase transition using an effective quark–meson model. We investigate the transition between infinite-volume and finite-volume scaling behavior when the system is placed in a finite box. We can estimate effects that the finite volume and the explicit symmetry breaking by the current quark masses have on the scaling behavior which is observed in full QCD lattice simulations. The model allows us to explore large quark masses as well as the chiral limit in a wide range of volumes, and extract information about the scaling regimes. In particular, we find large scaling deviations for physical pion masses and significant finite-volume effects for pion masses that are used in current lattice simulations.     

Monte Carlo studies of wilson loops in four-dimensional U(2) gauge theory

Wilson loops are calculated using Monte Carlo simulations for pure U(2) gauge theory on a 6⁴ lattice. The loops appear to contain an area law piece in both the high and low temperature regions. The string tension is discontinuous at β = β_c, where β_c is the critical inverse temperature. This suggests that the first-order phase transition in U(2) gauge theory is not a deconfining phase transition. The determinant of the Wilson loop, however, extracts the U(1) part of the theory and appears to lose the area law at low temperature.     

无费密子格点规范理论几种新作用量的探讨

我们提出了几种无费密子格点规范理论的新作用量形式,证明了它们符合Wilson对格点作用量提出的条件,讨论了它们与几种常用的作用量间的关系。并推导了在使用新作用量时Wilson圈满足的Schwinger-Dyson方程,证实了当N→∞时,E-K模型中的Schwinger-Dyson方程和标准格点模型相同。 关键词：     

Analytical Calculations of Large Wilson Loop Averages and String Tension in SU(2) Lattice Gauge Theory

Based on. the Schwinger-Dyson equation for a Wilson loop in the SU(2) lattice gauge theory, we evaluate approximately the averages of Wilson loop of size I × J, from which string tension of the theory has been extracted.     

Derivation and simulation of Langevin equations for the Wilson loop in the SU(N) lattice gauge theory

Within the framework of the stochastic quantization method, a general Langevin equation is derived for any function of link variables in the SU(N) lattice gauge theory. The Langevin equation for the Wilson loop is applied to numerical calculations of its expectation value. The same kind of simulation for the thermal Wilson loop is also carried out.     

Study of compact QED with light fermions

We present a numerical study of compact QED including dynamical fermions of mass = 0.10 (lattice units) on a 6⁴ lattice. Staggered lattice fermions and the Wilson action and mixed gauge actions were studied. The simulations used two modified hybrid methods: one with stochastic fields and the other with deterministic ones. Working with a variable number of flavors we found that the chiral transition which separates the strong and weak coupling phases is of first order in all cases. The strength of these discontinuous transitions increase with the number of flavors.     

The nature of the transition in d = 4 U(1) lattice gauge theory

The phase transition for the d = 4 compact U(1) lattice gauge theory has been studied using the Monte Carlo renormalization-group method. A single relevant eigenvalue is observed on the Wilson axis. The MCRG estimate for the exponent v changes with the coupling β; an extrapolation towards β^∞_c provides an estimate v ∼ 0.42 rather than ∼ 0.33 as obtained by finite-size scaling. It is confirmed that loops of monopole current are the mechanism driving the transition. It is shown that at the transition the largest loop of monopole current undergoes a discontinuity in size and begins to span the lattice. On the basis of these findings, it is conjectured that on the Wilson axis the discontinuity is a finite-size effect.     

Atomistic investigation of phase transition in solid argon induced by shock wave transmission

A molecular dynamics (MD) simulation is employed to study the phase transition process in argon induced by shock wave transmission. Deriving the relation between the shock and piston velocities, the theoretical equation of state for argon is presented. Also, argon equation of state is obtained by measuring the quantities directly from simulations to be able to detect the phase transitions. The phase transition is also detected by using argon phase diagram and free energy calculations. A comparison shows good agreement between the theoretical and MD results for the phase transitions. Based on these simulations, it is concluded that under a shock wave transmission with suitable energy, the solid argon experiences a phase transition from solid to liquid and another from liquid to supercritical fluid. By reflecting the shock wave back at the end of its passage, the whole argon may reach the supercritical state.     

Field theory on a non‐commutative plane: a non‐perturbative study

The 2d gauge theory on the lattice is equivalent to the twisted Eguchi–Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1‐ and 2‐point function of Wilson loops, as well as the 2‐point function of Polyakov lines. The 2‐point functions agree with a universal wave function renormalization. The large N double scaling limit corresponds to the continuum limit of non‐commutative gauge theory, so the observed large N scaling demonstrates the non‐perturbative renormalizability of this non‐commutative field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov‐Bohm effect in the presence of a constant magnetic field, identified with the inverse non‐commutativity parameter. Next we investigate the 3d λϕ⁴ model with two non‐commutative coordinates and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d = 4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns. We further present results for the correlators and the dispersion relation. In non‐commutative field theory the Lorentz invariance is explicitly broken, which leads to a deformation of the dispersion relation. In one loop perturbation theory this deformation involves an additional infrared divergent term. Our data agree with this perturbative result. We also confirm the recent observation by Ambjø rn and Catterall that stripes occur even in d = 2, although they imply the spontaneous breaking of the translation symmetry.     

A new model for confinement

We propose a new approach towards the understanding of confinement. Starting from an anisotropic five-dimensional pure gauge theory, we approach a second order phase transition where the system reduces dimensionally. Dimensional reduction is realized via localization of the gauge and scalar degrees of freedom on four-dimensional branes. The gauge coupling deriving from the brane Wilson loop observable runs like an asymptotically free coupling at short distance, while it exhibits clear signs of string formation at long distance. The regularization used is the lattice. We take the continuum limit by keeping the ratio of the lattice spacing in the brane over the lattice spacing along the extra dimension constant and smaller than one.     

The phase structure of lattice QCD with two flavors of Wilson quarks and renormalization group improved gluons

The effect of changing the lattice action for the gluon field on the recently observed [F. Farchioni, R. Frezzotti, K. Jansen, I. Montvay, G.C. Rossi, E. Scholz, A. Shindler, N. Ukita, C. Urbach, I. Wetzorke, Eur. Phys. J. C 39, 421 (2005); hep-lat/0406039] first order phase transition near zero quark mass is investigated by replacing the Wilson plaquette action by the DBW2 action. The lattice action for quarks is unchanged: it is in both cases the original Wilson action. It turns out that Wilson fermions with the DBW2 gauge action have a phase structure where the minimal pion mass and the jump of the average plaquette are decreased, when compared to Wilson fermions with Wilson plaquette action at similar values of the lattice spacing. Taking the DBW2 gauge action is advantageous also from the point of view of the computational costs of numerical simulations.Received: 29 October 2004, Revised: 7 March 2005, Published online: 31 May 2005     

高压下Al的零温电子结构和物态方程

 用LMTO法（线性Muffin-Tin轨道法），计算了金属铝的超高压电子结构及零温物态方程。Al的压缩比到10，压力达10 TPa。根据第一原理计算结果，在带结构方面，s带总是处于Fermi能以下，随着压力的增加，s、p和d的带宽增加，随后则杂化程度增加，所以s、d轨道的电子占据数连续变化。上述变化对压力的影响也是连续的，换言之，从s→d转变没有理由说明Al在0.5 TPa附近冲击Hugoniot的斜率的拐弯现象。而这一点则是与Altshuler的观点不同。物态方程的第一原理计算结果表明，bcc结构比fcc结构要软，但因差别不很大，即使发生fcc→bcc的转变，也不会引起Hugoniot的质的变化（拐弯）。Al的LMTO物态方程还表明，我们以前所采用的半经验的冷压误差可达30%。为此，根据LMTO结果，给出新的冷压表达式p=∑_i=0⁵a_iδ^i/3，δ=Ω₀/Ω，其中a₀=-7.327 79，a₁=18.754 3，a₂=10.209 7，a₃=-2.523 53，a₄=-4.787 2，a₅=6.065 94，拟合误差小于3%。     

The deconfining phase transition in lattice quantum chromodynamics

We present a large-scale Monte Carlo calculation of the deconfining phase transition temperature in lattice quantum chromodynamics without fermions. Using the Wilson action, the transition temperature as a function of the lattice couplingg is consistent with scaling behavior dictated by the perturbativeα function for 6/g²>6.15. Speaker at the conference; on leave from CRIP, Budapest.     

Correlation inequalities and quark confinement in lattice gauge theories

Some inequalities for the Wilson loop for Z₂ and U(N) lattice gauge theories are derived. They are used to show the area decay of the Wilson loop above a certain temperature. Possible use of such inequalities to prove the absence of a phase transition for the SU(2) case is discussed.     

Nonanalyticity in scale in the planar limit of QCD

Using methods of numerical lattice gauge theory we show that, in the limit of a large number of colors, properly regularized Wilson loops have an eigenvalue distribution which changes nonanalytically as the overall size of the loop is increased. This establishes a large-N phase transition in continuum planar gauge theory, a fact whose precise implications remain to be worked out.     

Topological susceptibility in lattice QCD with unimproved Wilson fermions

We address a long standing problem regarding topology in lattice simulations of QCD with unimproved Wilson fermions. Earlier attempt with unimproved Wilson fermions at β=5.6 to verify the suppression of topological susceptibility with decreasing quark mass (mq) was unable to unambiguously confirm the suppression. We carry out systematic calculations for two degenerate flavours at two different lattice spacings (β=5.6 and 5.8). The effects of quark mass, lattice volume and the lattice spacing on the spanning of different topological sectors are presented. We unambiguously demonstrate the suppression of the topological susceptibility with decreasing quark mass, expected from chiral Ward identity and chiral perturbation theory.     

Complex heavy-quark potential at finite temperature from lattice QCD

We calculate for the first time the complex potential between a heavy quark and antiquark at finite temperature across the deconfinement transition in lattice QCD. The real and imaginary part of the potential at each separation distance r is obtained from the spectral function of the thermal Wilson loop. We confirm the existence of an imaginary part above the critical temperature T(C), which grows as a function of r and underscores the importance of collisions with the gluonic environment for the melting of heavy quarkonia in the quark-gluon plasma.     

格点规范理论(Ⅰ)

本文介绍了由Wilson等人发展起来的处理粒子间强相互作用的格点规范理论。由于这个理论是建立在点阵上的规范理论,故首先讨论了点阵上体系的场论性质和统计物理性质之间的联系,介绍了处理粒子禁闭问题的Wilson判据,点阵的哈密顿形式。然后讨论了各种具体模型的计算方法,如规范场的点阵模型、紧致QED模型、费米子模型、阿贝尔Higgs模型等。在此基础上,总结出Wilson定理。本文也讨论了格点规范理论中的实空间重正化群方法,介绍了Heisenberg平面模型的重正化群分析,一维的二维的复现关系及Migdal近似。最后评介了近年来对于Wilson回路算子的一些研究,内容包括’t Hooft代数和Wilson回路算子方程等。