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Bernd A. Berg

Publications and source records attributed to Bernd A. Berg.

85 records · Page 5Linked to original sources
arXiv1997

Multi-Overlap Simulations of the $3d$ Edwards-Anderson Ising Spin Glass

We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for the entire $q$-range (multi-overlap) follow by re-weighting. We demonstrate the feasibility of the approach by studying the $3d$ Edwards-Anderson Ising ($J_{ik}=\pm 1$) spin glass in the broken phase ($β=1$). For the first time it becomes possible to obtain reliable results about spin glass tunneling barriers. In addition, as do some earlier numerical studies, our results support that Parisi mean field theory is valid down to $3d$.

cond-mat↗
arXiv1997

Algorithmic aspects of multicanonical simulations

Monte Carlo (MC) simulations of many systems, in particular those with conflicting constraints, can be considerably speeded up by using multicanonical or related methods. Some of these approaches sample with a-priori unknown weight factors. After introducing the concept, I shall focus on two aspects: (i) Opinions about the optimal choice of weight factors. (ii) Methods to get weight factor estimates, with emphasize on a multicanonical recursion.

hep-lat↗
arXiv1996

New Algorithm to Investigate Neural Networks

Random cost simulations were introduced as a method to investigate optimization problems in systems with conflicting constraints. Here I study the approach in connection with the training of a feed-forward multilayer perceptron, as used in high energy physics applications. It is suggested to use random cost simulations for generating a set of selected configurations. On each of those final minimization may then be performed by a standard algorithm. For the training example at hand many almost degenerate local minima are thus found. Some effort is spend to discuss whether they lead to equivalent classifications of the data.

hep-ph↗
arXiv1995

Schrödinger's Cat -- Amended

Arguments have been raised that the system--observer cut of quantum mechanics can be shifted arbitrarily close to, or even into, the conscious observer. Here I show that this view leads to {\it observable} contradictions (despite our inability to control the phases of macroscopic states). For this purpose I modify and extend Schrödinger's well--known superposition of a cat in its dead and alive state. Implications for other interpretations of quantum mechanics are also discussed. My conclusion is that quantum mechanics is incomplete. The question ``When does the state vector collapse?'' seems to be unavoidable, has observable consequences, and is not answered by quantum mechanics.

quant-ph↗
arXiv1995

Is There Quantum Gravity in Two Dimensions?

A hybrid model which allows to interpolate between the (original) Regge approach and dynamical triangulations is introduced. The gained flexibility in the measure is exploited to study dynamical triangulation in a fixed geometry. Our numerical results support KPZ exponents. A critical assessment concerning the apparent lack of gravitational effects in two dimensions follows.

hep-lat↗
arXiv1995

Multicanonical Recursions

The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.

hep-lat↗
arXiv1993

Grundstate Properties of the 3D Ising Spin Glass

We study zero--temperature properties of the 3d Edwards--Anderson Ising spin glass on finite lattices up to size $12^3$. Using multicanonical sampling we generate large numbers of groundstate configurations in thermal equilibrium. Finite size scaling with a zero--temperature scaling exponent $y = 0.74 \pm 0.12$ describes the data well. Alternatively, a descriptions in terms of Parisi mean field behaviour is still possible. The two scenarios give significantly different predictions on lattices of size $\ge 12^3$.

cond-mat↗
arXiv1993

Phase Structure of SU(2) Lattice Gauge Theory with Quantum Gravity

We investigate 4$d$ SU(2) lattice gauge theory with Regge--Einstein quantum gravity on a dynamically coupled Regge skeleton. To overview the phase diagram we perform simulations on a small $2\cdot 4^3$ system. Evidence for an entropy--dominated disordered, an entropy--dominated ordered and an ill--defined region is presented.

hep-lat↗
arXiv1992

Asymptotic Freedom and Euclidean Quantum Gravity

Pure SU(2) gauge theory is the simplest asymptotically free theory in four dimensions. To investigate Euclidean quantum gravity effects in a fundamental length scenario, we simulate 4$d$ SU(2) lattice gauge theory on a dynamically coupled Regge skeleton. The fluctuations of the skeleton are governed by the standard Regge-Einstein action. From a small $2\cdot 4^3$ lattice we report exploratory numerical results, limited to a region of strong gravity where the Planck mass and hadronic masses take similar orders of magnitude. We find a range of the Planck mass where stable bulk expectation values are obtained which vary smoothly with the gauge coupling, and a remnant of the QCD deconfining phase transition is located. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/krishnan (to go to that directory type: cd pub/krishnan) and is called gravity.ps (to get it type: get gravity.ps). If you have any problems send mail to krishnan@ds1.scri.fsu.edu.

hep-lat↗
arXiv1992

Monte Carlo Calculation of the Surface Free Energy for the 2d 7-state Potts Model, and an Estimate for 4d SU(3) Gauge Theory

Using the recently proposed multicanonical ensemble, we perform Monte Carlo simulation for the 2d 7-state Potts model and calculate its surface free energy density (surface tension) to be $2 f^s = 0.0241 \pm 0.0010$. This is an order of magnitude smaller than other estimates in the recent literature. Relying on existing Monte Carlo data, we also give a preliminary estimate for the surface tension of 4d SU(3) lattice gauge theory with $L_t=2$.

hep-lat↗
arXiv1992

A New Approach to Spin Glass Simulations

We present a recursive procedure to calculate the parameters of the recently introduced multicanonical ensemble and explore the approach for spin glasses. Temperature dependence of the energy, the entropy and other physical quantities are easily calculable and we report results for the zero temperature limit. Our data provide evidence that the large $L$ increase of the ergodicity time is greatly improved. The multicanonical ensemble seems to open new horizons for simulations of spin glasses and other systems which have to cope with conflicting constraints.

hep-lat↗