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Register a new userTwo-Dimensional Dynamical Triangulation using the Grand-canonical Ensemble
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The string susceptibility exponents of dynamically triangulated two dimensional surfaces with sphere and torus topology were calculated using the grand-canonical Monte Carlo method. We also simulated the model coupled to d-Ising spins (d=1,2,3,5).
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The string susceptibility exponents of dynamically triangulated 2-dimensional surfaces with various topologies, such as a sphere, torus and double-torus, were calculated by the grand-canonical Monte Carlo method. These simulations were made for surfaces coupled to $d$-Ising spins ($d$=0,1,2,3,5). In each simulation the area of surface was constrained to within 1000 to 3000 of triangles, while maintaining the detailed-balance condition. The numerical results show excellent agreement with theoretical predictions as long as $d leq 2$.
The gravitational dual to the grand canonical ensemble of a large $N$ holographic theory is a charged black hole. These spacetimes -- for example Reissner-Nordstrom-AdS -- can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations, Cauchy horizons never form. For certain irrelevant deformations, Cauchy horizons can exist at one specific temperature. We show that the scalar field triggers a rapid collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon. Finally, we make some observations on the interior of charged dilatonic black holes where the Kasner exponent at the singularity exhibits an attractor mechanism in the low temperature limit.
We discuss two new DoS approaches for finite density lattice QCD. The paper extends a recent presentation of the new techniques based on Wilson fermions, while here we now discuss and test the case of finite density QCD with staggered fermions. The first of our two approaches is based on the canonical formulation where observables at a fixed net quark number $N$ are obtained as Fourier moments of the vacuum expectation values at imaginary chemical potential $theta$. We treat the latter as densities which can be computed with the recently developed FFA method. The second approach is based on a direct grand canonical evaluation after rewriting the QCD partition sum in terms of a suitable pseudo-fermion representation. In this form the imaginary part of the pseudo-fermion action can be identified and the corresponding density may again be computed with FFA. We develop the details of the two approaches and discuss some exploratory first tests for the case of free fermions where reference results for assessing the new techniques may be obtained from Fourier transformation.
A thorough numerical examination for the field theory of 4D quantum gravity (QG) with a special emphasis on the conformal mode dependence has been studied. More clearly than before, we obtain the string susceptibility exponent of the partition function by using the Grand-Canonical Monte-Carlo method. Taking thorough care of the update method, the simulation is made for 4D Euclidean simplicial manifold coupled to $N_X$ scalar fields and $N_A$ U(1) gauge fields. The numerical results suggest that 4D simplicial quantum gravity (SQG) can be reached to the continuum theory of 4D QG. We discuss the significant property of 4D SQG.
Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small `solvation shells around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent `bath. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed.
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