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Related Experiment Video

Updated: Aug 24, 2025

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

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Published on: June 15, 2022

Binder ratio in the two-dimensional q-state clock model.

Luong Minh Tuan^1,2, Ta Thanh Long¹, Duong Xuan Nui^1,3

¹Advanced Institute for Science and Technology, Hanoi University of Science and Technology, Hanoi 10000, Vietnam.

Physical Review. E

|October 21, 2022

Summary

The two-dimensional q-state clock model shows two Kosterlitz-Thouless phase transitions for q=5,6 and one second-order transition for q=4. Critical temperatures were accurately estimated using Binder ratio analysis.

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Area of Science:

Statistical mechanics
Condensed matter physics

Background:

The two-dimensional q-state clock model is a fundamental system for studying phase transitions.
Understanding its critical behavior is crucial for theoretical physics.

Purpose of the Study:

To investigate the phase transition properties of the two-dimensional q-state clock model.
To determine the nature and number of phase transitions for different values of q.

Main Methods:

Extensive Monte Carlo simulations were employed.
Analysis of the Binder ratio and its temperature derivative was performed.

Main Results:

The model exhibits two distinct Kosterlitz-Thouless phase transitions for q=5 and q=6.
A single second-order phase transition was observed for q=4.
Critical temperatures were accurately estimated using Binder ratio crossing and derivative analysis.

Conclusions:

The study confirms the distinct phase transition behaviors of the q-state clock model based on the value of q.
The methods used provide accurate estimations of critical temperatures and insights into different phases.