Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data

• Authors: Per Lundow , Klas Markström
• Languages of publication: EN

Abstracts

EN

In this paper we discuss how partial knowledge of the density of states for a model can be used to give good approximations of the energy distributions in a given temperature range. From these distributions one can then obtain the statistical moments corresponding to e.g. the internal energy and the specific heat. These questions have gained interest apropos of several recent methods for estimating the density of states of spin models. As a worked example we finally apply these methods to the 3-state Potts model for cubic lattices of linear order up to 128. We give estimates of e.g. latent heat and critical temperature, as well as the micro-canonical properties of interest.

Keywords

EN

statistical physics; Monte Carlo method; phase transitions; Ising model; Potts model

Discipline

• 02.50.-r: Probability theory, stochastic processes, and statistics(see also section 05 Statistical physics, thermodynamics, and nonlinear dynamical systems)
• 02.70.-c: Computational techniques; simulations(for quantum computation, see 03.67.Lx; for computational techniques extensively used in subdivisions of physics, see the appropriate section; for example, see 47.11.-j Computational methods in fluid dynamics)
• 05.50.+q: Lattice theory and statistics (Ising, Potts, etc.)(see also 64.60.Cn Order-disorder transformations, and 75.10.Hk Classical spin models)
• 64.60.De: Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2009
• Volume: 7
• Issue: 3
• Pages: 490-502

Dates

published

1 - 9 - 2009

online

25 - 6 - 2009

Contributors

author

Per Lundow

• Department of theoretical physics, AlbaNova University Center, KTH, SE-106 91, Stockholm, Sweden

author

Klas Markström

• Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87, Umeå, Sweden

References

• [1] W. Janke, Physica A 254, 164 (1998) http://dx.doi.org/10.1016/S0378-4371(98)00014-4[Crossref]
• [2] J. Hove, Phys. Rev. E 70, 056707 (2004)
• [3] F. Wang, D. P. Landau, Phys. Rev. Let. 86, 2050 (2001) http://dx.doi.org/10.1103/PhysRevLett.86.2050[Crossref]
• [4] J.-S. Wang, R. H. Swendsen, J. Stat. Phys. 106, 245 (2002) http://dx.doi.org/10.1023/A:1013180330892[Crossref]
• [5] R. Häggkvist et al., J. Stat. Phys. 114, 455 (2004) http://dx.doi.org/10.1023/B:JOSS.0000003116.17579.5d[Crossref]
• [6] H. Touchette, E. Touchette, S. Richard, B. Turkington, Physica A 340, 138 (2004) http://dx.doi.org/10.1016/j.physa.2004.03.088[Crossref]
• [7] Ch. Junghans, M. Bachmann, W. Janke, Phys. Rev. Lett. 97, 218103 (2006)
• [8] A. M. Ferrenberg, D. P. Landau, R. H. Swendsen, Phys. Rev. E 5, 5092 (1995) http://dx.doi.org/10.1103/PhysRevE.51.5092[Crossref]
• [9] C. McDiarmid, Algorithms and Combinatorics 16, 195 (1998) [Crossref]
• [10] A. Martin-Löf, Commun. Math. Phys. 32, 75 (1973) http://dx.doi.org/10.1007/BF01646430[Crossref]
• [11] R. S. Ellis, Classics in Mathematics: Entropy, large deviations, and statistical mechanics, Reprint of the 1985 original (Springer-Verlag, Berlin, 2006)
• [12] B. Kaufman, Phys. Rev. 76, 1232 (1949) http://dx.doi.org/10.1103/PhysRev.76.1232[Crossref]
• [13] R. Häggkvist et al., Phys. Rev. E 69, 046104 (2004)
• [14] P. Beale, Phys. Rev. 76, 78 (1996)
• [15] C. Borgs, Proceedings of FOCS’ 99 (1999), www.math.cmu.edu/%7Eaf1p/papers.html
• [16] C. Borgs, R. Kotecký, I. Medved, J. Stat. Phys. 109, 67 (2002) http://dx.doi.org/10.1023/A:1019931410450[Crossref]
• [17] W. Janke, R. Villanova, Nucl. Phys. B 489, 679 (1997) http://dx.doi.org/10.1016/S0550-3213(96)00710-9[Crossref]
• [18] A. J. Guttmann, I. G. Enting, J. Phys. A 27, 5801 (1994) http://dx.doi.org/10.1088/0305-4470/27/17/014[Crossref]
• [19] Roland Häggkvist et al., Adv. Phys. 56, 653 (2007) http://dx.doi.org/10.1080/00018730701577548[Crossref]

Identifiers

DOI

10.2478/s11534-009-0033-9