Eur. Phys. J. B 6, 395-398 (1998)
https://doi.org/10.1007/s100510050566

Configuration space for random walk dynamics^*

¹ Department of Physics, The Florida State University, Tallahassee, FL 32306, USA and Supercomputer Computations Research Institute, Tallahassee, FL 32306, USA
² Department of Physics, Michigan Technological University, Houghton, MI 49931, USA

Corresponding authors: ^a berg@hep.fsu.edu - ^b hansmann@mta.edu

Received: 13 May 1998
Accepted: 26 May 1998
Published online: 15 December 1998

Abstract

Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a configuration to be sampled depends on a number of unusual quantities, which are explained in this paper. This has been overlooked in recent literature, where the method is advertised for the calculation of canonical expectation values. We illustrate these points for the 2d Ising model. In addition, we prove a previously conjectured equation which relates microcanonical expectation values to the spectral density.