First order phase transitions of the Potts model in fractal dimensions

Pascal Monceau

Physica A: Statistical Mechanics and its Applications, 2007, vol. 379, issue 2, 559-568

Abstract: The phase diagram of the q-state Potts model in fractal dimensions is studied with the help of Wang–Landau Monte Carlo simulations on Sierpinski and Menger fractal structures. A particular attention is paid to first order transitions just above the border separating the second order phase transition regime from the first order one. Although the translation invariance is strongly broken in deterministic fractals, evidence is given that such a deviation from the translational symmetry is not able to induce second order transitions for large values of q when the dimension lies between 1.9746 and 3. Moreover, the occurrence of second order transitions for very large values of q in the case of hierarchically weakly connected systems, that is when the fractal dimension is significantly smaller than 2, is pointed out. At last, the evolution of first order physical averages such as the latent heats and the interfacial free energies with the space dimensionality and the number of spin states is discussed.

Keywords: Fractals; Phase transitions; Potts model; Wang–Landau simulations (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437107000891
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:379:y:2007:i:2:p:559-568

DOI: 10.1016/j.physa.2007.01.009

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().