Spin models on random lattices

Wolfhard Janke, Desmond A Johnston and Ramon Villanova

Physica A: Statistical Mechanics and its Applications, 2000, vol. 281, issue 1, 207-220

Abstract: Under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a different behaviour than in the corresponding pure system. Here we discuss a series of Monte Carlo studies of a special type of such disordered systems, namely spin models defined on quenched, random lattices exhibiting geometrical disorder in the connectivity of the lattice sites. In two dimensions we present results for the q-state Potts model on random tri-valent (Φ3) planar graphs, which appear quite naturally in the dynamically triangulated random surface (DTRS) approach to quantum gravity, as well as on Poissonian random lattices of Voronoi/Delaunay type. Both cases, q⩽4 and >4, are discussed which, in the pure model without disorder, give rise to second- and first-order phase transitions, respectively. In three dimensions results for the Ising model on Poissonian random lattices are briefly described. We conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder, and a discussion of the distinguishing differences.

Keywords: Connectivity disorder; Random lattices; Gravity graphs; Potts model; Phase transitions; Monte Carlo simulations (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437100000145
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:281:y:2000:i:1:p:207-220

DOI: 10.1016/S0378-4371(00)00014-5

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 ().