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 Physics , 1999, DOI: 10.1016/S0920-5632(00)91796-1 Abstract: The phase transition of 4D simplicial quantum gravity coupled to U(1) gauge fields is studied using Monte-Carlo simulations. The phase transition of the dynamical triangulation model with vector field ($N_{V}=1$) is smooth as compared with the pure gravity($N_{V}=0$). The node susceptibility ($\chi$) is studied in the finite size scaling method. At the critical point, the node distribution has a sharp peak in contrast to the double peak in the pure gravity. From the numerical results, we expect that 4D simplicial quantum gravity with U(1) vector fields has higher order phase transition than 1st order, which means the possibility to take the continuum limit at the critical point.
 Sumati Surya Physics , 2011, DOI: 10.1088/0264-9381/29/13/132001 Abstract: We present evidence for a phase transition in a theory of 2D causal set quantum gravity which contains a dimensionless non-locality parameter $\epsilon \in (0,1]$. The transition is between a continuum phase and a crystalline phase, characterised by a set of covariant observables. For a fixed size of the causal set the transition temperature $\beta_c^{-1}$ decreases monotonotically with $\epsilon$. The line of phase transitions in the $\beta_c^2$ v/s $\epsilon$ plane asymptotes to the infinite temperature axis, suggesting that the continuum phase survives the analytic continuation.
 Physics , 1999, DOI: 10.1016/S0920-5632(00)91790-0 Abstract: The phase diagram of 2d Lorentzian quantum gravity (LQG) coupled to conformal matter is studied. A phase transition is observed at $c=c_{\rm crit}$ ($1/2  Physics , 1998, DOI: 10.1016/S0920-5632(99)85206-2 Abstract: Four-dimensional (4D) simplicial quantum gravity coupled to U(1) gauge fields has been studied using Monte-Carlo simulations. A negative string susceptibility exponent is observed beyond the phase-transition point, even if the number of vector fields (NV) is 1. We find a scaling relation of the boundary volume distributions in this new phase. This scaling relation suggests a fractal structure similar to that of 2D quantum gravity. Furthermore, evidence of a branched polymer-like structure is suggested far into the weak-coupling region, even for NV > 1. As a result, we propose new phase structures and discuss the possibility of taking the continuum limit in a certain region between the crumpled and branched polymer phases.  Physics , 1995, DOI: 10.1016/0920-5632(95)00363-E Abstract: We report a high statistics simulation of Ising spins coupled to 2D quantum gravity in the Regge calculus approach using triangulated tori with up to$512^2$vertices. For the constant area ensemble and the$dl/l$functional measure we definitively can exclude the critical exponents of the Ising phase transition as predicted for dynamically triangulated surfaces. We rather find clear evidence that the critical exponents agree with the Onsager values for static regular lattices, independent of the coupling strength of an$R^2$interaction term. For exploratory simulations using the lattice version of the Misner measure the situation is less clear.  Gabriele Gionti Physics , 1997, Abstract: We discuss the elongated phase of 4D simplicial quantum gravity by exploiting recent analytical results. In particular using Walkup's theorem we prove that the dominating configurations in the elongated phase are tree-like structures called "stacked spheres". Such configurations can be mapped into branched polymers and baby universes arguments are used in order to analyse the critical behaviour of theory in the weak coupling regime.  Physics , 1998, DOI: 10.1016/0038-1098(96)00424-3 Abstract: Path Integral Quantum Monte Carlo simulation is used to study thermodynamic properties and a phase diagram of 2D quantum Josephson array, described by 2+1 XY model. The helicity and vorticity moduli, correlation function of phases and other characteristics of the system as functions of quantum parameter$q$and temperature$T$are studied ($q=2e/\sqrt{JC_0}$,$J$is the Josephson coupling constant,$C_0$is the intragrain capacitance). Quantum fluctuation induced superconductor - normal phase transition is studied in detail through the use of behavior of above-mentioned quantities. No discontinuous or reentrant phase transition in$q-T$plane is found. Analysis of the vorticity and the renormalized coupling constant leads to the conclusion that the whole line of phase transition is of Kosterlitz - Thouless type.  Physics , 1996, DOI: 10.1016/S0920-5632(96)00770-0 Abstract: We present data indicating that the recent evidence for the phase transition being of first order does not result from a breakdown of the ergodicity of the algorithm. We also present data showing that the thermodynamical limit of the model is independent of topology.  Physics , 2014, DOI: 10.1016/j.physletb.2015.03.008 Abstract: We study matter with central charge$c >1$coupled to two-dimensional (2d) quantum gravity, here represented as causal dynamical triangulations (CDT). 2d CDT is known to provide a regularization of (Euclidean) 2d Ho\v{r}ava-Lifshitz quantum gravity. The matter fields are massive Gaussian fields, where the mass is used to monitor the central charge$c$. Decreasing the mass we observe a higher order phase transition between an effective$c=0$theory and a theory where$c>1$. In this sense the situation is somewhat similar to that observed for "standard" dynamical triangulations (DT) which provide a regularization of 2d quantum Liouville gravity. However, the geometric phase observed for$c >1\$ in CDT is very different from the corresponding phase observed for DT.