Monopole Condensation in Lattice SU(2) QCD

This is the short review of Monte-Carlo studies of quark confinement in lattice QCD. After abelian projections both in the maximally abelian and Polyakov gauges, it is seen that the monopole part alone is responsible for confinement. A block spin transformation on the dual lattice suggests that lattice $SU(2)$ QCD is always ( for all $\beta$) in the monopole condensed phase and so in the confinement phase in the infinite volume limit.Comment: Contribution to Confinement '95, March 1995, Osaka, Japan. Names of figure files are corrected. 8 page uuencoded latex file and 10 ps figure

Aging dynamics of ferromagnetic and reentrant spin glass phases in stage-2 Cu0.80_{0.80}C0.20_{0.20}Cl2_{2} graphite intercalation compound

Aging dynamics of a reentrant ferromagnet stage-2 Cu$_{0.8}$Co$_{0.2}$Cl$_{2}$ graphite intercalation compound has been studied using DC magnetic susceptibility. This compound undergoes successive transitions at the transition temperatures $T_{c}$ ($\approx 8.7$ K) and $T_{RSG}$ ($\approx 3.3$ K). The relaxation rate $S_{ZFC}(t)$ exhibits a characteristic peak at $t_{cr}$ below $T_{c}$. The peak time $t_{cr}$ as a function of temperature $T$ shows a local maximum around 5.5 K, reflecting a frustrated nature of the ferromagnetic phase. It drastically increases with decreasing temperature below $T_{RSG}$. The spin configuration imprinted at the stop and wait process at a stop temperature $T_{s}$ ($<T_{c}$) during the field-cooled aging protocol, becomes frozen on further cooling. On reheating, the memory of the aging at $T_{s}$ is retrieved as an anomaly of the thermoremnant magnetization at $T_{s}$. These results indicate the occurrence of the aging phenomena in the ferromagnetic phase ($T_{RSG}<T<T_{c}$) as well as in the reentrant spin glass phase ($T<T_{RSG}$).Comment: 9 pages, 9 figures; submitted to Physical Review

Slow quench dynamics of the Kitaev model: anisotropic critical point and effect of disorder

We study the non-equilibrium slow dynamics for the Kitaev model both in the presence and the absence of disorder. For the case without disorder, we demonstrate, via an exact solution, that the model provides an example of a system with an anisotropic critical point and exhibits unusual scaling of defect density $n$ and residual energy $Q$ for a slow linear quench. We provide a general expression for the scaling of $n$ ($Q$) generated during a slow power-law dynamics, characterized by a rate $\tau^{-1}$ and exponent $\alpha$, from a gapped phase to an anisotropic quantum critical point in $d$ dimensions, for which the energy gap $\Delta_{\vec k} \sim k_i^z$ for $m$ momentum components ($i=1..m$) and $\sim k_i^{z'}$ for the rest $d-m$ components ($i=m+1..d$) with $z\le z'$: $n \sim \tau^{-[m + (d-m)z/z']\nu \alpha/(z\nu \alpha +1)}$ ($Q \sim \tau^{-[(m+z)+ (d-m)z/z']\nu \alpha/(z\nu \alpha +1)}$). These general expressions reproduce both the corresponding results for the Kitaev model as a special case for $d=z'=2$ and $m=z=\nu=1$ and the well-known scaling laws of $n$ and $Q$ for isotropic critical points for $z=z'$. We also present an exact computation of all non-zero, independent, multispin correlation functions of the Kitaev model for such a quench and discuss their spatial dependence. For the disordered Kitaev model, where the disorder is introduced via random choice of the link variables $D_n$ in the model's Fermionic representation, we find that $n \sim \tau^{-1/2}$ and $Q\sim \tau^{-1}$ ($Q\sim \tau^{-1/2}$) for a slow linear quench ending in the gapless (gapped) phase. We provide a qualitative explanation of such scaling.Comment: 10 pages, 11 Figs. v

Various representations of infrared effective lattice QCD

We study various representations of the infrared effective theory of SU(2) gluodynamics starting from the monopole action derived recently. We determine the coupling constants in the abelian-Higgs model directly from lattice QCD and evaluate the type of the QCD vacuum. The string action is derived using the BKT transformation on the lattice. At the classical level this action reproduces the physical string tension with a good accuracy.Comment: 3 pages, LaTeX, 2 figures; talk presented at LATTICE9