Binder ratio in the two-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-state clock model
Luong Minh Tuan, Ta Thanh Long, Duong Xuan Nui, Pham Tuan Minh, Nguyen Duc Trung Kien, Dao Xuan Viet
Abstract
We study phase transition properties of the two-dimensional q-state clock model by an extensive Monte Carlo simulation. By analyzing the Binder ratio and its temperature derivative, we confirm that the two-dimensional q-state clock model exhibits two distinct Kosterlitz-Thouless phase transitions for q=5,6 but it has one second-order phase transition for q=4. The critical temperatures are estimated quite accurately from the crossing behavior of the Binder ratio (for q<5) and from negative divergent dips of the derivative of the Binder ratio (for q≥5) around these critical points. We also calculate the correlation length, the helicity modulus, and the derivative of the helicity modulus, and analyze their behaviors in different phases in detail.