Abstract
The Broad Histogram Method (BHMC) is a novel analysis technique for estimating the density of states from microcanonical averages related to some protocol of virtual movements. The method is completely general and can be applied in conjunction with many different Monte Carlo methods, including microcanonical, canonical and multicanonical simulations, to accelerate the estimation of the density of states, the specific heat, and similar thermodynamic quantities. In previous works [1,2] we proposed a way of extending the BHMC to systems with continuous degrees of freedom and applied these ideas to the study of the 3D XY-model. Here we summarize these ideas, present results for the 3D classical Heisenberg model, and show how to include an external field. Combined with microcanonical simulations the BHMC gives results for a very broad temperature range with computer efforts smaller than those required by five canonical Metropolis simulations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.D. Muñoz and H.J. Herrmann, Int. J. Mod. Phys. C (in print), also in cond-mat/9810024.
J.D. Muñoz and H.J. Herrmann, con-dmat/9810292.
P.M.C. de Oliveira, T.J.R Penna and H.J. Herrmann, Braz. J. of Phys. 26, 677–683 (1996); also in cond-mat/9610041.
P.M.C. de Oliveira, T.J.P. Penna and H.J. Herrmann, Eur. Phys. J. B 1, 205–208 (1998); also in cond-mat/9709064.
P.M.C. de Oliveira, Int. J. Mod. Phys. C 9, 497–503 (1998).
P.M.C. de Oliveira, Eur. Phys. J. B 6, 111–115 (1998).
B.A. Berg and U.H.E. Hansmann, Eur. Phys. J. B 6, 395–398 (1998).
J.-S. Wang, cond-mat/9810017, to appear in Eur. Phys. J. B.
B.A. Berg, Int. J. Mod. Phys. C 3, 1083–1098 (1992).
A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965) Chaps. 5–7.
The function ln(N dn(E)) changes slowly on the whole energy axis except at very low energies, which do not affect the temperatures we are interested in. Furthermore, we are taking Eb = 0.1% of the total energy. This justifies the approximation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag
About this paper
Cite this paper
Muňoz, J.D., Herrmann, H.J. (2000). Further Applications of the Broad Histogram Method for Continuous Systems. In: Landau, D.P., Lewis, S.P., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics XII. Springer Proceedings in Physics, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59689-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-59689-6_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64086-5
Online ISBN: 978-3-642-59689-6
eBook Packages: Springer Book Archive