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

I Balog¹, K Uzelac

¹Institute of Physics, P.O. Box 304, Bijenicka cesta 46, HR-10001 Zagreb, Croatia. balog@ifs.hr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 7, 2007

Summary

This study extends the invaded cluster approach to the 2D Potts model, identifying a tricritical point through simultaneous percolation events. Results align with known data for critical exponents and vacancy concentrations.

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Last Updated: Jul 13, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Spatial Separation of Molecular Conformers and Clusters

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Published on: January 9, 2014

Area of Science:

Statistical Mechanics
Computational Physics

Background:

The invaded cluster approach is a computational method used to study phase transitions.
The Potts model is a statistical mechanics model relevant to magnetism and other fields.
Annealed vacancies introduce disorder into the system, affecting its properties.

Purpose of the Study:

To extend the invaded cluster approach to the 2D Potts model with annealed vacancies.
To identify and locate the tricritical point in the system's parameter space.
To analyze the scaling properties and critical exponents near the tricritical point.

Main Methods:

Utilizing the random-cluster representation for the 2D Potts model.
Developing a novel algorithm based on geometrical arguments.
Simultaneously analyzing percolation of Fortuin-Kasteleyn clusters and geometrical disorder clusters.

Main Results:

The proposed algorithm converges to the tricritical point.
The tricritical point is characterized by the simultaneous onset of two types of percolation.
Accurate determination of the tricritical point location and vacancy concentrations for q=1,2,3.
Presentation of scaling properties and critical exponents.

Conclusions:

The extended invaded cluster approach effectively studies the 2D Potts model with annealed vacancies.
The identified tricritical point and its associated phenomena provide insights into phase transitions in disordered systems.
The findings are consistent with existing high-quality results, validating the method.