# Study of Cluster Fluctuations in Two-dimensional q-State Potts Model

## TL;DR

This study investigates cluster size fluctuations in the 2D q-State Potts Model across multiple states, revealing how cluster behavior varies with temperature and system size, and providing evidence for first-order phase transitions.

## Contribution

It introduces a cluster algorithm to analyze fluctuations and offers new insights into phase transition nature in the Potts Model.

## Key findings

- Cluster size fluctuations depend on temperature and number of states.
- Evidence for first-order transition in the model.
- Cluster analysis complements traditional measures for phase transition detection.

## Abstract

The two-dimensional Potts Model with 2 to 10 states is studied using a cluster algorithm to calculate fluctuations in cluster size as well as commonly used quantities like equilibrium averages and the histograms for energy and the order parameter. Results provide information about the variation of cluster sizes depending on the temperature and the number of states. They also give evidence for first-order transition when energy and the order parameter related measurables are inconclusive on small size lattices.