Invaded cluster algorithm for a tricritical point in a diluted Potts model

TL;DR

This paper extends the invaded cluster algorithm to a 2D Potts model with vacancies, successfully locating the tricritical point and analyzing its critical properties using geometrical and percolation concepts.

Contribution

The authors develop a novel invaded cluster algorithm for the diluted Potts model that accurately identifies the tricritical point in two dimensions.

Findings

Tricritical point accurately located for q=1, 2, 3

Good agreement with known results for vacancy concentration

Scaling properties and critical exponents characterized

Abstract

The invaded cluster approach is extended to 2D Potts model with annealed vacancies by using the random-cluster representation. Geometrical arguments are used to propose the algorithm which converges to the tricritical point in the two-dimensional parameter space spanned by temperature and the chemical potential of vacancies. The tricritical point is identified as a simultaneous onset of the percolation of a Fortuin-Kasteleyn cluster and of a percolation of "geometrical disorder cluster". The location of the tricritical point and the concentration of vacancies for q = 1, 2, 3 are found to be in good agreement with the best known results. Scaling properties of the percolating scaling cluster and related critical exponents are also presented.