Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-11-27
Nucl. Phys. B 700, 385 (2004)
Physics
Condensed Matter
Statistical Mechanics
23 pages, 11 figures, 2nd version: references added, introduction partly rewritten, error estimates improved
Scientific paper
10.1016/j.nuclphysb.2004.08.030
The tricritical behavior of the two-dimensional $q$-state Potts model with vacancies for $1\leq q \leq4$ is argued to be encoded in the fractal structure of the geometrical spin clusters of the pure model. The close connection between the critical properties of the pure model and the tricritical properties of the diluted model is shown to be reflected in an intimate relation between Fortuin-Kasteleyn and geometrical clusters: The same transformation mapping the two critical regimes onto each other also maps the two cluster types onto each other. The map conserves the central charge, so that both cluster types are in the same universality class. The geometrical picture is supported by a Monte Carlo simulation of the high-temperature representation of the Ising model ($q=2$). In this new numerical approach, closed graph configurations are generated by means of a Metropolis update algorithm, involving single plaquettes.
Janke Wolfhard
Schakel Adriaan M. J.
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